case study understanding quadrilaterals class 8

• Understanding Quadrilaterals Class 8 Assertion Reason Questions Maths Chapter 3

Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 8 maths. In this article, you will find assertion reason questions for CBSE Class 8 Maths Chapter 3 Understanding Quadrilaterals. It is a part of Assertion Reason Questions for CBSE Class 8 Maths Series.

Table of Contents

Assertion Reason Questions on Understanding Quadrilaterals

Questions :

Q. 1. Assertion (A): In a quadrilateral, there are 4 sides. Reason(R): A quadrilateral is a four-sided polygon, having four vertices and four edges. (a) Both A and R are true and R is the correct explanation of $A$ (b) Both $A$ and $R$ are true but $R$ is not the correct explanation of A (c) $A$ is true but $R$ is false (d) $A$ is false but $R$ is true

Difficulty Level: Medium

Ans. Option (a) is correct Explanation: Quadrilateral has 4 sides, 4 vertices and 4 edges.

Also read: Understanding Quadrilaterals Case Study Questions for Class 8

Q. 2. Assertion (A): All the parallelograms are rectangles. Reason(R): All the rhombuses are parallelograms. (a) Both $A$ and $R$ are true and $R$ is the correct explanation of $A$ (b) Both $A$ and $R$ are true but $R$ is not the correct explanation of A (c) $A$ is true but $R$ is false (d) $A$ is false but $R$ is true

Ans. Option (d) is correct Explanation: All parallelograms are not rectangles, but all rhombuses are parallelograms.

Linear Equations in One Variable Class 8 Assertion Reason Questions Maths Chapter 2

Rational numbers class 8 assertion reason questions maths chapter 1, you may also like.

• Case Study Questions for CBSE Class 8 Maths

Download eBooks for CBSE Class 8 Maths Understanding Quadrilaterals

• Understanding Quadrilaterals Topicwise Worksheet for CBSE Class 8 Maths

Topics from which assertion reason questions may be asked

• Convex and Concave Polygons.
• Regular and Irregular Polygons.
• Sum of Measures of the Exterior Angles of a Polygon.
• Kinds of QuadrilateralTrapezium; Kite; Parallelogram.
• Some Special ParallelogramsRhombus; Rectangle; Square.

Assertion reason questions from the above given topic may be asked.

Download Customised White Label Study Materials in MS Word Format

We are providing teaching resources to teachers and coaching institute looking for customised study materials in MS word format. Our High-quality editable study material which is prepared by the expert faculties are Highly useful for Teachers, Mentors, Tutors, Faculties, Coaching Institutes, Coaching Experts, Tuition Centers.

Frequently Asked Questions (FAQs) on Understanding Quadrilaterals Assertion Reason Questions Class 8

Q1: what are assertion reason questions.

A1: Assertion-reason questions consist of two statements: an assertion (A) and a reason (R). The task is to determine the correctness of both statements and the relationship between them. The options usually include: (i) Both A and R are true, and R is the correct explanation of A. (ii) Both A and R are true, but R is not the correct explanation of A. (iii) A is true, but R is false. (iv) A is false, but R is true. or A is false, and R is also false.

Q2: Why are assertion reason questions important in Maths?

A2: Students need to evaluate the logical relationship between the assertion and the reason. This practice strengthens their logical reasoning skills, which are essential in mathematics and other areas of study.

Q3: How can practicing assertion reason questions help students?

A3: Practicing assertion-reason questions can help students in several ways: Improved Conceptual Understanding:  It helps students to better understand the concepts by linking assertions with their reasons. Enhanced Analytical Skills:  It enhances analytical skills as students need to critically analyze the statements and their relationships. Better Exam Preparation:  These questions are asked in exams and practicing them can improve your performance.

Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies: Understand Each Statement Separately:  Determine if each statement is true or false independently. Analyze the Relationship:  If both statements are true, check if the reason correctly explains the assertion.

Q5: What are common mistakes to avoid when answering Assertion Reason questions?

A5: Common mistakes include: Not reading the statements carefully and missing key details. Assuming the Reason explains the Assertion without checking the logical connection. Confusing the order or relationship between the statements. Overthinking and adding information not provided in the question.

Q6: What resources can help me practice Assertion Reason Questions for Class 8 Maths?

A6: Use study guides specifically designed for Assertion-Reason questions. Online educational platforms and reference books for Class 8 Maths also offer practice questions and explanations. xamcontent.com also provides assertion reason questions for cbse class 8 maths.

Q7: How do you classify quadrilaterals based on their properties?

A7: Quadrilaterals can be classified based on their properties such as sides, angles, and diagonals. For example: (1) Parallelograms have opposite sides that are equal and parallel. (2) Rhombuses have all four sides equal in length. (3) Rectangles have all angles equal to 90 degrees.

Q8: Can a quadrilateral have equal sides and angles but still not be a square?

A8: Yes, a rhombus can have all sides equal and opposite angles equal, but its angles need not be right angles, unlike in a square.

Q9: What is the difference between a square and a rhombus?

A9: A square is a type of rhombus with all four sides equal and all angles equal to 90 degrees. However, a rhombus may have all sides equal but not necessarily all angles equal to 90 degrees.

Q10: Are there any online resources or tools available for practicing linear equations in one variable assertion reason questions?

A10: A9: We provide assertion reason questions for CBSE Class 8 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit  Physics Gurukul  website. they are having a large collection of case study questions for all classes.

Related Posts

• School Solutions
• Star Program
• NCERT Solutions Class 12 Maths
• NCERT Solutions Class 12 Physics
• NCERT Solutions Class 12 Chemistry
• NCERT Solutions Class 12 Biology
• NCERT Solutions Class 12 Commerce
• NCERT Solutions Class 12 Economics
• NCERT Solutions Class 12 Accountancy
• NCERT Solutions Class 12 English
• NCERT Solutions Class 12 Hindi
• NCERT Solutions Class 11 Maths
• NCERT Solutions Class 11 Physics
• NCERT Solutions Class 11 Chemistry
• NCERT Solutions Class 11 Biology
• NCERT Solutions Class 11 Commerce
• NCERT Solutions Class 11 Accountancy
• NCERT Solutions Class 11 English
• NCERT Solutions Class 11 Hindi
• NCERT Solutions Class 11 Statistics
• NCERT Solutions Class 10 Maths
• NCERT Solutions Class 10 Science
• NCERT Solutions Class 10 English
• NCERT Solutions Class 10 Hindi
• NCERT Solutions Class 10 Social Science
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 8 Maths
• NCERT Solutions Class 8 Science
• NCERT Solutions Class 8 English
• NCERT Solutions Class 8 Hindi
• NCERT Solutions Class 8 Social Science
• NCERT Solutions Class 7 Maths
• NCERT Solutions Class 7 Science
• NCERT Solutions Class 7 English
• NCERT Solutions Class 7 Hindi
• NCERT Solutions Class 7 Social Science
• NCERT Solutions Class 6 Maths
• NCERT Solutions Class 6 Science
• NCERT Solutions Class 6 English
• NCERT Solutions Class 6 Hindi
• NCERT Solutions Class 6 Social Science
• NCERT Solutions Class 5 Maths
• NCERT Solutions Class 5 English
• NCERT Solutions Class 5 EVS
• NCERT Solutions Class 4 Maths
• NCERT Solutions Class 4 English
• NCERT Solutions Class 4 EVS
• NCERT Solutions Class 4 Hindi
• NCERT Solutions Class 3 Maths
• NCERT Solutions Class 3 English
• NCERT Solutions Class 3 EVS
• NCERT Solutions Class 3 Hindi
• NCERT Solutions Class 2 Maths
• NCERT Solutions Class 2 English
• NCERT Solutions Class 2 Hindi
• NCERT Solutions Class 1 Maths
• NCERT Solutions Class 1 English
• NCERT Solutions Class 1 Hindi
• NCERT Books Class 12
• NCERT Books Class 11
• NCERT Books Class 10
• NCERT Books Class 9
• NCERT Books Class 8
• NCERT Books Class 7
• NCERT Books Class 6
• NCERT Books Class 5
• NCERT Books Class 4
• NCERT Books Class 3
• NCERT Books Class 2
• NCERT Books Class 1
• Important Questions Class 12
• Important Questions Class 11
• Important Questions Class 10
• Important Questions Class 9
• Important Questions Class 8
• Important Questions Class 7
• important questions class 6
• CBSE Class 12 Revision Notes
• CBSE Class 11 Revision Notes
• CBSE Class 10 Revision Notes
• CBSE Class 9 Revision Notes
• CBSE Class 8 Revision Notes
• CBSE Class 7 Revision Notes
• CBSE Class 6 Revision Notes
• CBSE Class 12 Syllabus
• CBSE Class 11 Syllabus
• CBSE Class 10 Syllabus
• CBSE Class 9 Syllabus
• CBSE Class 8 Syllabus
• CBSE Class 7 Syllabus
• CBSE Class 6 Syllabus
• CBSE Class 5 Syllabus
• CBSE Class 4 Syllabus
• CBSE Class 3 Syllabus
• CBSE Class 2 Syllabus
• CBSE Class 1 Syllabus
• CBSE Sample Question Papers For Class 12
• CBSE Sample Question Papers For Class 11
• CBSE Sample Question Papers For Class 10
• CBSE Sample Question Papers For Class 9
• CBSE Sample Question Papers For Class 8
• CBSE Sample Question Papers For Class 7
• CBSE Sample Question Papers For Class 6
• CBSE Sample Question Papers For Class 5
• CBSE Sample Question Papers For Class 4
• CBSE Sample Question Papers For Class 3
• CBSE Sample Question Papers For Class 2
• CBSE Sample Question Papers For Class 1
• CBSE Previous Year Question Papers Class 12
• CBSE Previous Year Question Papers Class 10
• Extra Questions For Class 8 Maths
• Extra Questions For Class 8 Science
• Extra Questions For Class 9 Maths
• Extra Questions For Class 9 Science
• Extra Questions For Class 10 Maths
• Extra Questions For Class 10 Science
• NEET 2021 Question Paper
• NEET 2020 Question Paper
• NEET 2019 Question Paper
• NEET 2018 Question Paper
• NEET 2017 Question Paper
• NEET 2016 Question Paper
• NEET 2015 Question Paper
• NEET Physics Questions
• NEET Chemistry Questions
• NEET Biology Questions
• NEET Sample Papers
• NEET Physics Syllabus
• NEET Chemistry Syllabus
• NEET Biology Syllabus
• NEET Mock Test
• NEET Eligibility Criteria
• JEE Main 2021 Question Paper
• JEE Main 2020 Question Paper
• JEE Main 2019 Question Paper
• JEE Main 2018 Question Paper
• JEE Main 2017 Question Paper
• JEE Main 2016 Question Paper
• JEE Main 2015 Question Paper
• JEE Main Sample Papers
• JEE Main Physics Syllabus
• JEE Main Chemistry Syllabus
• JEE Main Maths Syllabus
• JEE Main Physics Questions
• JEE Main Chemistry Questions
• JEE Main Maths Questions
• JEE main revision notes
• JEE Main Mock Test
• JEE Advanced Physics Questions
• JEE Advanced Chemistry Questions
• JEE Advanced Maths Questions
• JEE Advanced 2021 Question Paper
• JEE Advanced 2020 Question Paper
• JEE Advanced 2019 Question Paper
• JEE Advanced 2018 Question Paper
• JEE Advanced 2017 Question Paper
• JEE Advanced 2016 Question Paper
• JEE Advanced 2015 Question Paper
• JEE Advanced Physics Syllabus
• JEE Advanced Chemistry Syllabus
• JEE Advanced Maths Syllabus
• JEE Advanced Mock Test
• ISC Class 12 Syllabus
• ISC Class 11 Syllabus
• ICSE Class 10 Syllabus
• ICSE Class 9 Syllabus
• ICSE Class 8 Syllabus
• ICSE Class 7 Syllabus
• ICSE Class 6 Syllabus
• ISC Sample Question Papers for Class 12
• ISC Sample Question Papers for Class 11
• ICSE Sample Question Papers for Class 10
• ICSE Sample Question Papers for Class 9
• ICSE Sample Question Papers for Class 8
• ICSE Sample Question Papers for Class 7
• ICSE Sample Question Papers for Class 6
• ICSE Class 10 Revision Notes
• ICSE Class 9 Revision Notes
• ISC Important Questions for Class 12
• ISC Important Questions for Class 11
• ICSE Important Questions for Class 10
• ICSE Important Questions for Class 9
• ICSE Important Questions for Class 8
• ICSE Important Questions for Class 7
• ICSE Important Questions for Class 6
• ISC Class 12 Question Paper
• ICSE Class 10 Question Paper
• Maharashtra Board Syllabus
• Maharashtra Board Sample Question Paper
• Maharashtra Board Previous Year Question Paper
• AP Board Syllabus
• AP Board Sample Question Paper
• AP Board Previous Year Question Paper
• Tamilnadu Board Syllabus
• Tamilnadu Board Sample Question Paper
• Tamilnadu Board Previous Year Question Paper
• Telangana Board Syllabus
• Telangana Board Sample Question Paper
• Telangana Board Previous Year Question Paper
• Karnataka Board Syllabus
• Karnataka Board Sample Question Paper
• Karnataka Board Previous Year Question Paper
• Examination Full Forms
• Physics Full Forms
• Chemistry Full Forms
• Biology Full Forms
• Educational Full Form
• CUET Eligibility Criteria
• CUET Exam Pattern
• CUET Cutoff
• CUET Syllabus
• CUET Admit Card
• CUET Counselling
• CUET Previous Year Question Papers
• CUET Application Form
• CUET Sample Papers
• CUET Exam Centers
• CUET Exam Dates
• CUET Results
• Physics Formulas
• Chemistry Formulas
• Math Formulas
• Algebra Formulas
• Geometry Formulas
• Trigonometry Formulas
• Subscription

Important Questions Class 8 Maths Chapter 3

Home » CBSE » Important Questions Class 8 Maths Chapter 3

• CBSE Important Questions
• Important Questions Class 6
• CBSE Previous Year Question Papers
• CBSE Revision Notes
• CBSE Syllabus
• CBSE Extra Questions
• CBSE Sample Papers
• ISC & ICSE Syllabus
• ICSE Syllabus Class 9
• ICSE Syllabus Class 8
• ICSE Syllabus Class 7
• ICSE Syllabus Class 6
• ICSE Syllabus Class 10
• ICSE Question Paper
• ICSE Sample Question Papers
• ISC Sample Question Papers For Class 12
• ISC Sample Question Papers For Class 11
• ICSE Sample Question Papers For Class 10
• ICSE Sample Question Papers For Class 9
• ICSE Sample Question Papers For Class 8
• ICSE Sample Question Papers For Class 7
• ICSE Sample Question Papers For Class 6
• ICSE Revision Notes
• ICSE Important Questions
• ISC Important Questions For Class 12
• ISC Important Questions For Class 11
• ICSE Important Questions For Class 10
• ICSE Important Questions For Class 9
• ICSE Important Questions For Class 8
• ICSE Important Questions For Class 7
• ICSE Important Questions For Class 6
• Maharashtra board
• Rajasthan-Board
• Andhrapradesh Board
• AP Board syllabus
• Telangana Board
• Tamilnadu Board
• Tamilnadu Sample Question Paper
• Tamilnadu Syllabus
• Tamilnadu Previous Year Question Paper
• NCERT Solutions Class 12
• NCERT Solutions Class 10
• NCERT Solutions Class 11
• NCERT Solutions Class 9
• NCERT Solutions Class 8
• NCERT Solutions Class 7
• NCERT Solutions Class 6
• NCERT Solutions Class 5
• NCERT Solutions Class 4
• NCERT Solutions Class 3
• NCERT Solutions Class 2
• NCERT Solutions Class 1
• JEE Main Question Papers
• JEE Main Syllabus
• JEE Main Questions
• JEE Main Revision Notes
• JEE Advanced Question Papers
• JEE Advanced Syllabus
• JEE Advanced Questions
• JEE Advanced Sample Papers
• NEET Question Papers
• Neet 2021 Question Paper
• Neet 2020 Question Paper
• Neet 2019 Question Paper
• Neet 2018 Question Paper
• Neet 2017 Question Paper
• Neet 2016 Question Paper
• Neet 2015 Question Paper
• NEET Syllabus

Important Questions Class 8 Mathematics Chapter 3 – Understanding Quadrilaterals

Mathematics deals with numbers of various forms, shapes, logic, quantity and arrangements. Mathematics also teaches us to solve problems based on numerical calculations and find solutions.

Quick Links

Chapter 3 of Class 8 Mathematics is called ‘Understanding Quadrilaterals’. A quadrilateral is a closed shape and also a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of all the interior angles of a quadrilateral is always equal to 360 degrees. In a quadrilateral, the sides are straight lines and are two-dimensional. Square, rectangle, rhombus, parallelogram, etc., are examples of quadrilaterals. The formula for the angle sum of a polygon = (n – 2) × 180°.

Extramarks is the best study buddy for students and helps them with comprehensive online study solutions from Class 1 to Class 12. Our team of expert Mathematics teachers have prepared a variety of NCERT solutions to help students in their studies and exam preparation. Students can refer to our Important Questions Class 8 Mathematics Chapter 3 to practise exam-oriented questions. We have collated questions from various sources such as NCERT textbooks and exemplars, CBSE sample papers, CBSE past year question papers, etc. Students can prepare well for their exams and tests by solving a variety of chapter questions from our Important Questions Class 8 Mathematics Chapter 3.

To ace their exams, students can register on the Extramarks website to access Class 8 Mathematics Chapter 3 important questions, CBSE extra questions, Mathematics formulas, and much more.

Important Questions Class 8 Mathematics Chapter 3 – With Solution

Mentioned below are some sets of questions and their answers from our Chapter 3 Class 8 Mathematics important questions.

Question 1: A quadrilateral has three acute angles, each measuring 80°. What is the measure of the fourth angle of the quadrilateral?

Answer 1: – Let x be the measure of the fourth angle of a quadrilateral.

 The sum of all the angles of a quadrilateral + 360°

80° + 80° + 80° + x = 360° …………(since the measure of all the three acute angles = 80°)

 240° + x = 360°

x = 360° – 240°

Hence, the fourth angle made by the quadrilateral is 120°.

Question 2: Find the measure of all the exterior angles of a regular polygon with 

                        (i) 9 sides and (ii) 15 sides.

Answer 2 : (i) Total measure of all exterior angles = 360° 

                    Each exterior angle =sum of exterior angle = 360° = 40°

                                                           number of sides 9                                              

                    Each exterior angle = 40°

                   (ii) Total measure of all exterior angles = 360° 

                      Each exterior angle = sum of exterior angle =360° = 24° 

                                                            number of sides 15

                      Each exterior angle = 24° 

Answer 3: a) The sum of all the angles of the triangle = 180°

                       One side of a triangle

                       = 180°- (90° + 30°) = 60°

                        In a linear pair, the sum of two adjacent angles altogether measures up to 180° 

                       x + 90° = 180° 

                       x = 180° – 90° 

                          = 90° 

                       Similarly,

                       y + 60° = 180°

                       y = 180° – 60°

                           = 120°

                       similarly,

                      z + 30° = 180° 

                     z = 180° – 30° 

                        = 150°

                     Hence,x + y + z 

                                = 90° + 120° + 150° 

                                = 360°

                  Thus, the sum of the angles x, y, and z is altogether 360°

• b) Sum of all angles of quadrilateral = 360°

                 One side of quadrilateral = 360°- (60° + 80° + 120°) = 360° – 260° = 100°

                 x + 120° = 180°

                 x = 180° – 120°

                    = 60°

                y + 80° = 180° 

                y = 180° – 80° 

                  = 100°

                 z + 60° = 180°

                 z = 180° – 60° 

                   = 120°

                w + 100° = 180° 

                w = 180° – 100° = 80°

                x + y + z + w = 60° + 100° + 120° + 80° = 360°

Question 4: Adjacent sides of a rectangle are in the ratio 5: 12; if the perimeter of the given rectangle is 34 cm, find the length of the diagonal.

Answer 4: The ratio of the adjacent sides of the rectangle is 5: 12

                    Let 5x and 12x be adjacent sides.

                    The perimeter is the sum of all the given sides of a rectangle.

                     5x + 12x + 5x + 12x = 34 cm ……(since the opposite sides of the rectangle are the 

                                                                               same)

                     34x = 34

                      x = 34/34

                      x = 1 cm

                      Therefore, the adjacent sides of the rectangle are 5 cm and 12 cm, respectively.

                       That is,

                       Length =12 cm

                       Breadth = 5 cm

                       Length of the diagonal = √( l2 + b2)

                                                                 = √( 122 + 52)

                                                                 = √(144 + 25)

                                                                 = √169

                                                                 = 13 cm

                      Hence, the length of the diagonal of a rectangle is 13 cm.

Question 5: How many sides do regular polygons consist of if each interior angle is 165 ° ?

Answer 5: A regular polygon with an interior angle of 165°

                   We need to find the sides of the given regular polygon:-

                   The sum of all exterior angles of any given polygon is 360°.

                    Formula Used: Number of sides = 360∘ /Exterior angle

                            Exterior angle=180∘−Interior angle

                   Thus,

                   Each interior angle =165°

                   Hence, the measure of every exterior angle will be

                    =180°−165°

                    =15°

                   Therefore, the number of sides of the given polygon will be

                  =360°/15°

                   =24° 

Question 6: Find x in the following figure.

Answer 6: The two interior angles in the given figures are right angles = 90°

70° + m = 180°

 m = 180° – 70° 

(In a linear pair, the sum of two adjacent angles altogether measures up to 180°)

60° + n = 180° 

 n = 180° – 60° 

     = 120°

 The given figure has five sides, and it is a pentagon.

Thus, the sum of the angles of the pentagon = 540° 

 90° + 90° + 110° + 120° + y = 540°

410° + y = 540° 

y = 540° – 410° = 130°

x + y = 180°….. (Linear pair)

x + 130° = 180°

x = 180° – 130° 

Question 7: ABCD is a parallelogram with ∠A = 80°. The internal bisectors of ∠B and ∠C meet each other at O. Find the measure of the three angles of ΔBCO.

Answer 7: The measure of angle A = 80°.

                    In a parallelogram, the opposite angles are the same.

                    Hence,

                    ∠A = ∠C = 80°

                    And

                    ∠OCB = (1/2) × ∠C

                    = (1/2) × 80°

                    = 40°

              ∠B = 180° – ∠A (the sum of interior angles situated on the same side of the transversal is supplementary)

                     = 180° – 80°

                     = 100°

                     Also,

              ∠CBO = (1/2) × ∠B

              ∠CBO= (1/2) × 100°

              ∠CBO= 50°. 

             By the property of the sum of the angle BCO, we get,

            ∠BOC + ∠OBC + ∠CBO = 180°

            ∠BOC = 180° – (∠OBC + CBO)

                        = 180° – (40° + 50°)

                        = 180° – 90°

                        = 90°

      Hence, the measure of all the angles of triangle BCO is 40°, 50° and 90°.

Question 8: The measure of the two adjacent angles of the given parallelogram is the ratio of 3:2. Then, find the measure of each angle of the parallelogram.

Answer 8:  A parallelogram with adjacent angles in the ratio of 3:2

 To find:- The measure of each of the angles of the parallelogram.

                     Let the measure of angle A be 3x

                     Let the measure of angle B be 2x

Since the sum of the measures of adjacent angles is 180° for a parallelogram,

 3x+2x=180°

 ∠A=∠C =3x=108°

∠B=∠D =2x=72° (Opposite angles of a parallelogram are equal).

Hence, the angles of a parallelogram are 108°, 72°,108°and 72°

Question 9: Is it ever possible to have a regular polygon, each of whose interior angles is 100?

Answer 9: The sum of all the exterior angles of a regular polygon is 360°

As we also know, the sum of interior and exterior angles are 180°

Exterior angle + interior angle = 180-100=80°

When we divide the exterior angle, we will get the number of exterior angles

since it is a regular polygon means the number of exterior angles equals the number of sides.

Therefore n=360/ 80=4.5

And we know that 4.5 is not an integer, so having a regular polygon is impossible.

Whose exterior angle is 100°

Question 10: ABCD is a parallelogram in which ∠A=110 ° . Find the measure of the angles B, C and D, respectively.

Answer 10: The measure of angle A=110°

the sum of all adjacent angles of a parallelogram is 180°

∠A + ∠B = 180

110°+ ∠B = 180°

∠B = 180°- 110°

      = 70°.

Also ∠B + ∠C = 180° [Since ∠B and ∠C are adjacent angles]

70°+ ∠C = 180°

∠C = 180°- 70°

        = 110°.

Now ∠C + ∠D = 180° [Since ∠C and ∠D are adjacent angles]

110o+ ∠D = 180°

∠D = 180°- 110°

        = 70°

Question11: A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.

Answer 11: Let ABCD be the rhombus.

                   All the sides of a rhombus are the same.

                   Thus, AB = BC = CD = DA.

                  The side and diagonal of a rhombus are equal.

                  AB = BD 

                  Therefore, AB = BC = CD = DA = BD 

                  Consider triangle ABD,

                  Each side of a triangle ABD is congruent.

                  Hence, ΔABD is an equilateral triangle.

                  Similarly,

                  ΔBCD is also an equilateral triangle.

                  Thus, ∠BAD = ∠ABD = ∠ADB = ∠DBC = ∠BCD = ∠CDB = 60°

                  ∠ABC = ∠ABD + ∠DBC = 60° + 60° = 120°

                  And

                  ∠ADC = ∠ADB + ∠CDB = 60° + 60° = 120°

     Hence, all angles of the given rhombus are 60°, 120°, 60° and 120°, respectively.

Question 12: The two adjacent angles of a parallelogram are the same. Find the measure of each and every angle of the parallelogram.

Answer 12: A parallelogram with two equal adjacent angles.

To find:- the measure of each of the angles of the parallelogram.

The sum of all the adjacent angles of a parallelogram is supplementary.

∠B = ∠A = 90°

In a parallelogram, the opposite sides are the same.

Hence, each angle of the parallelogram measures 90°.

Question 13: The measures of the two adjacent angles of a parallelogram are in the given ratio 3: 2. Find the measure of every angle of the parallelogram.

Answer 13: Let the measures of two adjacent angles ∠A and ∠B be 3x and 2x, respectively, in parallelogram ABCD.

∠A + ∠B = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

The opposite sides of a parallelogram are the same.

∠A = ∠C = 3x = 3 × 36° = 108°

∠B = ∠D = 2x = 2 × 36° = 72°

Question 14: State whether true or false.

(a) All the rectangles are squares.

(b) All the rhombuses are parallelograms.

(c) All the squares are rhombuses and also rectangles.

(d) All the squares are not parallelograms.

(e) All the kites are rhombuses.

(f) All the rhombuses are kites.

(g) All the parallelograms are trapeziums.

(h) All the squares are trapeziums.

Answer 14: (a) This statement is false.

Since all squares are rectangles, all rectangles are not squares.

                     (b) This statement is true.

                     (c) This statement is true.

                     (d) This statement is false.

                     Since all squares are parallelograms, the opposite sides are parallel, and opposite angles are 

                     congruent.

                    (e) This statement is false.

                     Since, for example, the length of the sides of a kite is not the same length.

                     (f) This statement is true.

                     (g) This statement is true.

                     (h) This statement is true.

Question 15: Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?

Answer 15: Let ∠A and ∠B be two adjacent angles.

But we know that the sum of adjacent angles of a parallelogram is 180o

But given that ∠A = ∠B

Now substituting, we get

∠A + ∠A = 180°

∠A=180/2 = 90°

Question 16:Triangle ABC is a right-angled triangle, and O is the midpoint of the side opposite to the right angle. State why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

Answer 16: AD and DC are drawn in such a way that AD is parallel to BC 

and AB is parallel to DC

AD = BC and AB = DC

ABCD is a rectangle since the opposite sides are equal and parallel to each other, and the measure of all the interior angles is altogether 90°.

In a rectangle, all the diagonals bisect each other and are of equal length. 

Therefore, AO = OC = BO = OD

Hence, O is equidistant from A, B and C.

Question 17: Is the quadrilateral ABCD a parallelogram if

 (i) the measure of angle D + the measure of angle B = 180°?

 (ii) AB = DC = 8 cm , the length of AD = 4 cm and the length of BC = 4.4 cm?

(iii)The measure of angle A = 70° and the measure of angle C = 65°?

Answer 17: (i) Yes, the quadrilateral ABCD can be a parallelogram if ∠D + ∠B = 180° but it should also fulfil certain conditions, which are as follows:

(a) The sum of all the adjacent angles should be 180°.

(b) Opposite angles of a parallelogram must be equal.

(ii) No, opposite sides should be of the same length. Here, AD ≠ BC

(iii) No, opposite angles should be of the same measures. ∠A ≠ ∠C

Question 18: Find the measure of angles P and S if SP and RQ are parallel. 

Answer 18: ∠P + ∠Q = 180° (angles on the same side of transversal)

 ∠P + 130° = 180°

 ∠P = 180° – 130° = 50°

also, ∠R + ∠S = 180° (angles on the same side of transversal)

⇒ 90° + ∠S = 180°

⇒ ∠S = 180° – 90° = 90°

Thus, ∠P = 50° and ∠S = 90°

Yes, there is more than one method to find m∠P.

PQRS is a quadrilateral. The sum of measures of all angles is 360°.

Since we know the measurement of ∠Q, ∠R and ∠S.

∠Q = 130°, ∠R = 90° and ∠S = 90°

∠P + 130° + 90° + 90° = 360°

⇒ ∠P + 310° = 360°

⇒ ∠P = 360° – 310° = 50°

Question 19: The opposite angles of a parallelogram are (3x + 5)° and (61 – x)°. Find the measure of four angles.

Answer 19: (3x + 5)° and (61 – x)° are the opposite angles of a parallelogram.

The opposite angles of a parallelogram are the same. 

Therefore, (3x + 5)° = (61 – x)°

                    3x + x = 61° – 5°

                    4x = 56°

                    x = 56°/4

                    x = 14°

The first angle of the parallelogram =3x + 5

                                                               = 3(14) + 5 

                                                               = 42 + 5 = 47°

The second angle of the parallelogram=61 – x 

                                                                     = 61 – 14 = 47°

The measure of angles adjacent to the given angles = 180° – 47° = 133°

Hence, the measure of the four angles of the parallelogram is 47°, 133°, 47°, and 133°.

Question 20: What is the maximum exterior angle possible for a regular polygon?

Answer 20:   To find:- The maximum exterior angle possible for a regular polygon.

A polygon with minimum sides is an equilateral triangle.

So, the number of sides =3

The sum of all exterior angles of a polygon is 360°

Exterior angle =360°/Number of sides 

Therefore, the maximum exterior angle possible will be

Benefits of Solving Important Questions Class 8 Mathematics Chapter 3

Mathematics demands a lot of practice. Class 8, 9 and 10 are very important for students to develop a strong fundamental knowledge of Algebra as well as Geometry. We recommend that students get access to Extramarks comprehensive set of Important Questions Class 8 Mathematics Chapter 3. By regularly solving questions and going through our answer solutions, students will gain good confidence to solve complex problems from the Understanding Quadrilaterals chapter.

Below are a few benefits of frequently solving NCERT textbook and NCERT exemplar questions for Class 8.

• Our experienced Mathematics subject teachers have carefully assembled the most important questions Class 8 Mathematics Chapter 3 by analysing many past exam questions.
• Mathematics Class 8 Chapter 3 important questions provide information about the types of questions that may be asked in exams, which helps to minimise stress and exam anxiety. 
• The questions and solutions provided are based on the latest CBSE syllabus and as per CBSE guidelines. So the students can completely count on it.
• Studying something just once may help you grasp the concepts, but going over it again will help you remember it. You enhance your chances of getting good grades on exams while you solve more important questions Class 8 Mathematics Chapter 3. 
• The questions covered in our set of Important Questions Class 8 Mathematics Chapter 3 are based on various topics covered in the Quadrilaterals chapter. So while solving these questions, students will be able to revise the chapter and also clear any doubts they have.
• By solving our important questions Class 8 Mathematics Chapter 3, students will get a gist of how the paper will be prepared. Practising questions similar to the exam questions would help the students gain confidence, perform better in their exams, and eventually ace them.

Extramarks provides comprehensive learning solutions for students from Class 1 to Class 12. We have other study resources on our website, along with important questions and solutions. Students can also click on the below-mentioned links and access some of these resources:

• NCERT books
• CBSE syllabus
• CBSE sample papers
• CBSE previous year’s question papers
• Important formulas 
• CBSE extra questions
• Click to share on Facebook (Opens in new window)
• Click to share on Twitter (Opens in new window)
• Click to share on LinkedIn (Opens in new window)
• Click to share on WhatsApp (Opens in new window)

FAQs (Frequently Asked Questions)

1. what can i get from the extramarks website.

 Extramarks is one of the best educational platforms as it has its own archive of educational resources, which assists students in acing their exams. You can get all the NCERT-related material like NCERT solutions, solved exemplar solutions, NCERT-based mock tests, CBSE revision notes, and important questions Class 8 Mathematics Chapter 3 on the Extramarks website. Apart from this, you can get comprehensive guidance from our subject experts and doubt-clearing sessions once you sign up on our official website for any study resources.  

2. How can I score well in Class 8 Mathematics exams?

Mathematics requires a lot of practice. To score, one must have a strong conceptual understanding of the chapter, be good with numbers and calculations, practice Important Questions Class 8 Mathematics Chapter 3 regularly, give practice tests from time to time, get feedback and avoid silly mistakes. Regular practice with discipline will surely help the student to ace their exams.

3. How many types of quadrilaterals are there?

There are six basic types of quadrilaterals.

• Parallelogram

Fill this form to view question paper

Otp verification.

• Class 6 Maths
• Class 6 Science
• Class 6 Social Science
• Class 6 English
• Class 7 Maths
• Class 7 Science
• Class 7 Social Science
• Class 7 English
• Class 8 Maths
• Class 8 Science
• Class 8 Social Science
• Class 8 English
• Class 9 Maths
• Class 9 Science
• Class 9 Social Science
• Class 9 English
• Class 10 Maths
• Class 10 Science
• Class 10 Social Science
• Class 10 English
• Class 11 Maths
• Class 11 Computer Science (Python)
• Class 11 English
• Class 12 Maths
• Class 12 English
• Class 12 Economics
• Class 12 Accountancy
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Computer Science (Python)
• Class 12 Physical Education
• GST and Accounting Course
• Excel Course
• Tally Course
• Finance and CMA Data Course
• Payroll Course

Interesting

• Learn English
• Learn Excel
• Learn Tally
• Learn GST (Goods and Services Tax)
• Learn Accounting and Finance
• GST Tax Invoice Format
• Accounts Tax Practical
• Tally Ledger List
• GSTR 2A - JSON to Excel

Are you in school ? Do you love Teachoo?

We would love to talk to you! Please fill this form so that we can contact you

You are learning...

Chapter 3 Class 8 Understanding Quadrilaterals

Click on any of the links below to start learning from Teachoo ...

Updated for new NCERT Book .

Get NCERT Solutions of Chapter 3 Class 8 Understanding Quadrilaterals free at teachoo. Answers to all exercise questions and examples have been solved, with concepts of the chapter explained.

In this chapter, we will learn

• What are curves , open curves, closed curves, simple curves
• What are polygons , Different Types of Polygons
• Diagonal of a Polygon
• Convex and Concave Polygons
• Regular and Irregular Polygons
• Angle Sum Property of Polygons
• Sum of Exterior Angles of a Polygon
• Exterior Angles of a Regular Polygon
• What is a Quadrilateral
• Parallelogram
• Parallelogram propertie s - Opposite Angles are equal, Opposite sides are equal, Adjacent Angles are supplementary, Diagonals Bisect Each other
• Rhombus, Rectangle, Square are all parallelograms with additional properties

To learn from the NCERT, click on an exercise or example link below to get started.

To learn the Teachoo (टीचू) way, click on a concept below Concept Wise. In Concept Wise, first the concept is explained, and then the questions of that concept is solved - from easy to difficult

Note : When you click on a link, the first question or topic will open. To see other questions, there is a list with all the questions and concepts (it has arrows). You can refer to the list for other questions.

Click on a link now to begin.

Serial order wise

Concept wise.

What's in it?

Hi, it looks like you're using AdBlock :(

Please login to view more pages. it's free :), solve all your doubts with teachoo black.

Class 8 Maths Chapter 3 Important Question Answers - Understanding Quadrilaterals

Q1: What is the maximum exterior angle possible for a regular polygon? Sol:   To find:-  The maximum exterior angle possible for a regular polygon. A polygon with minimum sides is an equilateral triangle. So, the number of sides = 3 The sum of all exterior angles of a polygon is 360° Exterior angle = 360°/Number of sides  Therefore, the maximum exterior angle possible will be = 360°/3 = 120°

Q2: Find the measure of angles P and S if SP and RQ are parallel.  Sol:   ∠P + ∠Q = 180° (angles on the same side of transversal) ∠P + 130° = 180° ∠P = 180° – 130° = 50° also, ∠R + ∠S = 180° (angles on the same side of transversal) ⇒ 90° + ∠S = 180° ⇒ ∠S = 180° – 90° = 90° Thus, ∠P = 50° and ∠S = 90° Yes, there is more than one method to find m∠P. PQRS is a quadrilateral. The sum of measures of all angles is 360°. Since we know the measurement of ∠Q, ∠R and ∠S. ∠Q = 130°, ∠R = 90° and ∠S = 90° ∠P + 130° + 90° + 90° = 360° ⇒ ∠P + 310° = 360° ⇒ ∠P = 360° – 310°  = 50°

Sol:  AD and DC are drawn in such a way that AD is parallel to BC   and AB is parallel to DC AD = BC and AB = DC ABCD is a rectangle since the opposite sides are equal and parallel to each other, and the measure of all the interior angles is altogether 90°. In a rectangle, all the diagonals bisect each other and are of equal length.  Therefore, AO = OC = BO = OD Hence, O is equidistant from A, B and C. Q4: State whether true or false. (a) All the rectangles are squares. (b) All the rhombuses are parallelograms. (c) All the squares are rhombuses and also rectangles. (d) All the squares are not parallelograms. (e) All the kites are rhombuses. (f) All the rhombuses are kites. (g) All the parallelograms are trapeziums. (h) All the squares are trapeziums. Sol: (a)  This statement is false. A rectangle has opposite sides equal and all angles equal to 90 degrees, but for it to be a square, all four sides must be equal. Therefore, not all rectangles are squares.

(b) This statement is true.

A rhombus is a type of parallelogram where all four sides are of equal length. Since it has both pairs of opposite sides parallel, it is always a parallelogram. 

(c)  This statement is true.

A square has all properties of a rhombus (all sides equal) and a rectangle (all angles 90 degrees). Therefore, all squares are both rhombuses and rectangles.

(d)  This statement is false.

A square is a specific type of parallelogram where all sides are equal and all angles are right angles. Therefore, all squares are parallelograms.

(e)  This statement is false.

A kite has two pairs of adjacent sides equal, but not all four sides need to be equal. For it to be a rhombus, all four sides must be equal. Therefore, not all kites are rhombuses.

(f) This statement is true.

A rhombus has all four sides equal, which satisfies the condition of a kite having two pairs of adjacent sides equal. Therefore, all rhombuses are kites. 

(g)  This statement is false.

A parallelogram has both pairs of opposite sides parallel, and a trapezium is a quadrilateral with exactly one pair of parallel sides. Since parallelograms have two pairs of parallel sides, they do not meet this criterion and are not considered trapeziums. 

(h)  This statement is true.

A square has both pairs of opposite sides parallel, which means it satisfies the condition of a trapezium having at least one pair of parallel sides. Therefore, all squares are trapeziums. 

Q5: The two adjacent angles of a parallelogram are the same. Find the measure of each and every angle of the parallelogram. Sol:  A parallelogram with two equal adjacent angles. To find:-  the measure of each of the angles of the parallelogram. The sum of all the adjacent angles of a parallelogram is supplementary. ∠A + ∠B = 180° 2∠A = 180° ∠A = 90° ∠B = ∠A = 90° In a parallelogram, the opposite sides are the same. Therefore, ∠C = ∠A = 90° ∠D = ∠B = 90° Hence, each angle of the parallelogram measures 90°. Q6: ABCD is a parallelogram in which ∠A = 110 ° . Find the measure of the angles B, C and D, respectively. Sol:  The measure of angle A = 110° the sum of all adjacent angles of a parallelogram is 180° ∠A + ∠B = 180 110°+ ∠B = 180° ∠B = 180°- 110° = 70°. Also ∠B + ∠C = 180° [Since ∠B and ∠C are adjacent angles] 70° + ∠C = 180° ∠C = 180°- 70° = 110°. Now ∠C + ∠D = 180° [Since ∠C and ∠D are adjacent angles] 110° + ∠D = 180° ∠D = 180°- 110° = 70° Q7: The measure of the two adjacent angles of the given parallelogram is the ratio of 3:2. Then, find the measure of each angle of the parallelogram. Sol:   A parallelogram with adjacent angles in the ratio of 3:2  To find:-  The measure of each of the angles of the parallelogram. Let the measure of angle A be 3x Let the measure of angle B be 2x Since the sum of the measures of adjacent angles is 180° for a parallelogram, ∠A+∠B=180° 3x+2x=180° 5x=180° x=36° ∠A=∠C =3x=108° ∠B=∠D =2x=72° (Opposite angles of a parallelogram are equal). Hence, the angles of a parallelogram are 108°, 72°,108°and 72°

Q7: Find x in the following figure. Sol:  The two interior angles in the given figures are right angles = 90° 70° + m = 180° m = 180° – 70°  = 110° (In a linear pair, the sum of two adjacent angles altogether measures up to 180°) 60° + n = 180°  n = 180° – 60°  = 120° (In a linear pair, the sum of two adjacent angles altogether measures up to 180° The given figure has five sides, and it is a pentagon. Thus, the sum of the angles of the pentagon = 540°  90° + 90° + 110° + 120° + y = 540° 410° + y = 540° y = 540° – 410° = 130° x + y = 180°….. (Linear pair) x + 130° = 180° x = 180° – 130°  = 50°

Q8: Adjacent sides of a rectangle are in the ratio 5: 12; if the perimeter of the given rectangle is 34 cm, find the length of the diagonal. Sol:  The ratio of the adjacent sides of the rectangle is 5: 12 Let 5x and 12x be adjacent sides. The perimeter is the sum of all the given sides of a rectangle. 5x + 12x + 5x + 12x = 34 cm ……(since the opposite sides of the rectangle are the  same) 34x = 34 x = 34/34 x = 1 cm Therefore, the adjacent sides of the rectangle are 5 cm and 12 cm, respectively. That is, Length =12 cm Breadth = 5 cm Length of the diagonal = √( l2 + b2) = √( 122 + 52) = √(144 + 25) = √169 = 13 cm Hence, the length of the diagonal of a rectangle is 13 cm.

Q9: Find the measure of all the exterior angles of a regular polygon with  (i) 9 sides and  (ii) 15 sides. Sol:  (i)  Total measure of all exterior angles = 360°  Each exterior angle =sum of exterior angle = 360° = 40° number of sides 9                                               Each exterior angle = 40° (ii)  Total measure of all exterior angles = 360°  Each exterior angle = sum of exterior angle =360° = 24°  number of sides 15 Each exterior angle = 24° 

Q10: A quadrilateral has three acute angles, each measuring 80°. What is the measure of the fourth angle of the quadrilateral? Sol: – Let x be the measure of the fourth angle of a quadrilateral. The sum of all the angles of a quadrilateral + 360° 80° + 80° + 80° + x = 360° …………(since the measure of all the three acute angles = 80°)  240° + x = 360° x = 360° – 240° x = 120° Hence, the fourth angle made by the quadrilateral is 120°. Q11: How many sides do regular polygons consist of if each interior angle is 165 ° ? Sol:  A regular polygon with an interior angle of 165° We need to find the sides of the given regular polygon:- The sum of all exterior angles of any given polygon is 360°. Formula Used: Number of sides = 360 ∘ /Exterior angle Exterior angle = 180 ∘ −Interior angle Thus, Each interior angle = 165° Hence, the measure of every exterior angle will be = 180° − 165° = 15° Therefore, the number of sides of the given polygon will be = 360°/15° = 24°  Q12: ABCD is a parallelogram with ∠A = 80°. The internal bisectors of ∠B and ∠C meet each other at O. Find the measure of the three angles of ΔBCO. Sol:  The measure of angle A = 80°. In a parallelogram, the opposite angles are the same. Hence, ∠A = ∠C = 80° And ∠OCB = (1/2) × ∠C = (1/2) × 80° = 40° ∠B = 180° – ∠A (the sum of interior angles situated on the same side of the transversal is supplementary) = 180° – 80° = 100° Also, ∠CBO = (1/2) × ∠B ∠CBO= (1/2) × 100° ∠CBO= 50°.  By the property of the sum of the angle BCO, we get, ∠BOC + ∠OBC + ∠CBO = 180° ∠BOC = 180° – (∠OBC + CBO) = 180° – (40° + 50°) = 180° – 90° = 90° Hence, the measure of all the angles of triangle BCO is 40°, 50° and 90°. Q13: Is it ever possible to have a regular polygon, each of whose interior angles is 100? Sol:  The sum of all the exterior angles of a regular polygon is 360° As we also know, the sum of interior and exterior angles are 180° Exterior angle + interior angle = 180 - 100 = 80° When we divide the exterior angle, we will get the number of exterior angles  since it is a regular polygon means the number of exterior angles equals the number of sides. Therefore n = 360/ 80 = 4.5 And we know that 4.5 is not an integer, so having a regular polygon is impossible. Whose exterior angle is 100° Q14: A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus. Sol:  Let ABCD be the rhombus. All the sides of a rhombus are the same. Thus, AB = BC = CD = DA. The side and diagonal of a rhombus are equal. AB = BD  Therefore, AB = BC = CD = DA = BD  Consider triangle ABD, Each side of a triangle ABD is congruent. Hence, ΔABD is an equilateral triangle. Similarly, ΔBCD is also an equilateral triangle. Thus, ∠BAD = ∠ABD = ∠ADB = ∠DBC = ∠BCD = ∠CDB = 60° ∠ABC = ∠ABD + ∠DBC = 60° + 60° = 120° And ∠ADC = ∠ADB + ∠CDB = 60° + 60° = 120° Hence, all angles of the given rhombus are 60°, 120°, 60° and 120°, respectively. Q15: The measures of the two adjacent angles of a parallelogram are in the given ratio 3: 2. Find the measure of every angle of the parallelogram. Sol:  Let the measures of two adjacent angles ∠A and ∠B be 3x and 2x, respectively, in parallelogram ABCD. ∠A + ∠B = 180° ⇒ 3x + 2x = 180° ⇒ 5x = 180° ⇒ x = 36° The opposite sides of a parallelogram are the same. ∠A = ∠C = 3x = 3 × 36° = 108° ∠B = ∠D = 2x = 2 × 36° = 72°

Top Courses for Class 8

FAQs on Class 8 Maths Chapter 3 Important Question Answers - Understanding Quadrilaterals

practice quizzes

Viva questions, shortcuts and tricks, video lectures, study material, past year papers, previous year questions with solutions, mock tests for examination, extra questions, objective type questions, sample paper, semester notes, important questions.

Important Questions: Understanding Quadrilaterals Free PDF Download

Importance of important questions: understanding quadrilaterals, important questions: understanding quadrilaterals notes, important questions: understanding quadrilaterals class 8, study important questions: understanding quadrilaterals on the app.

Welcome Back

Create your account for free.

Forgot Password

Unattempted tests, change country, practice & revise.

NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals

NCERT solutions for class 8 maths chapter 3 understanding quadrilaterals define a polygon as a simple closed curve that is made up of straight lines. Thus, a quadrilateral can be defined as a polygon that has four sides, four angles, and four vertices. This chapter starts by introducing children to some very important concepts that they need to learn before moving on to studying quadrilaterals . These topics include the classification of polygons on the basis of sides, examining diagonals , concave, convex, regular, and irregular polygons as well as the angle sum property. The scope of NCERT solutions class 8 maths chapter 3 is very vast as there are several properties and types of quadrilaterals available. However, the explanation given in these solutions helps to simplify the learning process ensuring that students can build a strong geometrical foundation. 

Class 8 maths NCERT solutions chapter 3 elaborates on special quadrilaterals such as squares , rectangles , parallelograms , kites , and rhombuses . They show kids how to solve problems based on these figures and intelligently utilize the associated properties to remove the complexities from such questions. In the NCERT solutions Chapter 3 Understanding Quadrilaterals we will take an in-depth look at the basic elements and theories of these four-sided polygons and also you can find some of these in the exercises given below.

• NCERT Solutions Class 8 Maths Chapter 3 Ex 3.1
• NCERT Solutions Class 8 Maths Chapter 3 Ex 3.2
• NCERT Solutions Class 8 Maths Chapter 3 Ex 3.3
• NCERT Solutions Class 8 Maths Chapter 3 Ex 3.4

NCERT Solutions for Class 8 Maths Chapter 3 PDF

Using the NCERT solutions class 8 maths children can solidify several concepts of quadrilaterals. They understand the conditions under which a special quadrilateral such as a parallelogram becomes a square, how to find the measure of an interior or exterior angle , and so on. The links to all these brief and precise solutions are given below and kids can use them to improve their mathematical acumen.

☛ Download Class 8 Maths NCERT Solutions Chapter 3 Understanding Quadrilaterals

NCERT Class 8 Maths Chapter 3   Download PDF

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Quadrilaterals form a vital shape contributing to geometrical studies. Thus, children need to develop a robust conceptual foundation as they will require it in higher classes for solving more complicated problems and constructing this figure. They can do this by revising the solutions given above regularly. The following sections deal with an exercise-wise detailed analysis of NCERT Solutions Class 8 Maths Chapter 3 understanding quadrilaterals.

• Class 8 Maths Chapter 3 Ex 3.1 - 7 Questions
• Class 8 Maths Chapter 3 Ex 3.2 - 6 Questions
• Class 8 Maths Chapter 3 Ex 3.3 - 12 Questions
• Class 8 Maths Chapter 3 Ex 3.4 - 6 Questions

☛ Download Class 8 Maths Chapter 3 NCERT Book

Topics Covered: Identifying the polygon, finding the measure of angles, and verifying the exterior angles of a polygon are topics under class 8 maths NCERT solutions chapter 3. Apart from this, there are many sections dealing with the various elements of trapeziums , parallelograms, rectangles, squares, etc.

Total Questions: There are a total of 31 fantastic sums in Class 8 maths chapter 3 Understanding Quadrilaterals. 7 are simple theory-based problems, 16 are in-between and 8 are higher-order thinking sums.

List of Formulas in NCERT Solutions Class 8 Maths Chapter 3

The questions in the NCERT solutions class 8 maths chapter 3 are not only based on some formulas but also see the use of various vital properties. The sum of interior and exterior angles , along with theorems give the keys to attempting these sums. The angle sum property states that the sum of all the interior angles of a polygon is a multiple of the number of triangles that make up that polygon. Such pointers covered in NCERT solutions for class 8 maths chapter 3 make up the crux of this lesson and are given below.

• Angle Sum Property of a Quadrilateral: a + b + c + d = 360°. (a, b, c, d are the interior angles).
• The opposite sides and opposite angles of a parallelogram are equal in length.
• The adjacent angles in a parallelogram are supplementary.
• The diagonals of a parallelogram bisect each other.
• The diagonals of a rhombus are perpendicular bisectors of one another.

Important Questions for Class 8 Maths NCERT Solutions Chapter 3

NCERT Solutions for Class 8 Maths Video Chapter 3

FAQs on NCERT Solutions Class 8 Maths Chapter 3

Do i need to practice all questions provided in ncert solutions class 8 maths understanding quadrilaterals.

All the sums in the NCERT Solutions Class 8 Maths Understanding Quadrilaterals cover different subtopics of the lesson. These sums also pave a foundation for the geometrical topics in grades that are to follow. Thus, it is crucial for kids to practice all questions so as to get a clear idea of all the components in a quadrilateral.

What are the Important Topics Covered in Class 8 Maths NCERT Solutions Chapter 3?

Each exercise is based on a different topic such as angles of a polygon, rhombus, square, and rectangles; thus, each section that falls under the NCERT Solutions Class 8 Maths Chapter 3 must be given equal importance. Kids need to strategize their studies to focus more on learning properties and then applying them to questions.

How Many Questions are there in NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals?

There are a total of 31 questions in the NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals that are distributed among 4 exercises. There are different types of questions such as true and false sums, identifying the type of shape based on certain properties, and finding the measure of a particular angle using formulas.

What are the Important Formulas in Class 8 Maths NCERT Solutions Chapter 3?

Formulas such as the angle sum property of a quadrilateral, exterior angle property of a polygon, and other associated theories form the foundation of the NCERT Solutions Class 8 Maths Chapter 3. Students must spend a good amount of time practicing questions so as to get a good understanding of their application.

How CBSE Students can utilize NCERT Solutions Class 8 Maths Chapter 3 effectively?

To effectively utilize NCERT Solutions Class 8 Maths Chapter 3 it is advised that students go through the theory and solved examples associated with each exercise. They should then try to attempt the problem on their own. Finally, to get the best out of these solutions kids should cross-check their answers and go through the steps so that they can organize their answers in a well-structured manner.

Why Should I Practice NCERT Solutions Class 8 Maths Understanding Quadrilaterals Chapter 3?

The only way to ensure that a student has perfected his knowledge of a chapter is by practicing the questions periodically. The NCERT Solutions Class 8 Maths Understanding Quadrilaterals Chapter 3 has been given by experts with certain tips included to simplify the problems. By regular revision, kids will be confident with the topic and can get an amazing score in their examination.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Understanding Quadrilaterals Class 8 Extra Questions Maths Chapter 3

July 7, 2019 by Sastry CBSE

Extra Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Understanding Quadrilaterals Class 8 Extra Questions Very Short Answer Type

Question 4. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle. Solution: Sum of all interior angles of a quadrilateral = 360° Let the angles of the quadrilateral be 2x°, 3x°, 5x° and 8x°. 2x + 3x + 5x + 8x = 360° ⇒ 18x = 360° ⇒ x = 20° Hence the angles are 2 × 20 = 40°, 3 × 20 = 60°, 5 × 20 = 100° and 8 × 20 = 160°.

Understanding Quadrilaterals Class 8 Extra Questions Short Answer Type

Question 15. Write true and false against each of the given statements. (a) Diagonals of a rhombus are equal. (b) Diagonals of rectangles are equal. (c) Kite is a parallelogram. (d) Sum of the interior angles of a triangle is 180°. (e) A trapezium is a parallelogram. (f) Sum of all the exterior angles of a polygon is 360°. (g) Diagonals of a rectangle are perpendicular to each other. (h) Triangle is possible with angles 60°, 80° and 100°. (i) In a parallelogram, the opposite sides are equal. Solution: (a) False (b) True (c) False (d) True (e) False (f) True (g) False (h) False (i) True

Understanding Quadrilaterals Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Extra Questions for Class 8 Maths

Ncert solutions for class 8 maths, free resources.

NCERT Solutions

Quick Resources

Talk to our experts

1800-120-456-456

Class 8 Revision Notes for CBSE Maths Chapter 3 Understanding Quadrilaterals (Free PDF Download)

• Revision Notes
• Chapter 3 Understanding Quadrilaterals

Revision Notes for CBSE Class 8 Maths Chapter 3 - Free PDF Download

Revision Notes for CBSE Class 8 Mathematics Chapter 3 Understanding Quadrilaterals are quite useful for swiftly reviewing the whole chapter on exam days. In the form of a summary, the revision notes encompass all essential formulae and concepts presented in the chapter. Students do not need to be concerned about the large chapters to be covered during test time; simply refer to the revision notes and they are finished.

Well qualified faculties at Vedantu have designed CBSE Class 8 Maths Notes for Chapter 3 Understanding Quadrilaterals in such a way that the whole chapter is covered in a short summary. Vedantu’s revision notes cover all the important concepts and formulas related to quadrilaterals. Students can no doubt depend upon these revision notes while revising the chapters during the exam time.  If you wish to have an overview of a chapter at a glance, Vedantu revision notes will do this for you. Vedantu is a platform that provides free NCERT Solution and other study materials for students. Download Class 8 Maths NCERT Solutions and NCERT Solutions for Class 8 Science to help you to revise complete syllabus ans score more marks in your examinations.

Important Topics Covered in CBSE Class 8 Maths Chapter 3 Understanding Quadrilaterals 

The below list contains the important topics of the CBSE Class 8 Maths Chapter 3, which have appeared at least once in previous years’ examinations. So, students must go through these thoroughly while preparing for the upcoming exams.

Introduction to Plane Surfaces

Classification of Polygons

Convex and Concave Polygons

Regular and Irregular Polygons

Angle Sum Property in Quadrilaterals 

Sum of the Measures of the Exterior Angles of a Polygon

Types of Quadrilaterals

Parallelogram

 Elements of a Parallelogram

 Angles of a Parallelogram

Diagonals of a Parallelogram

Some Special Parallelograms

Download CBSE Class 8 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 8 Maths revision notes for All chapters:

Access Class 8 Maths Chapter 3 - Understanding Quadrilaterals Notes in 30 Minutes

Parallelogram: 

A quadrilateral with each pair of opposite sides parallel.

Opposite sides are equal. 

Opposite angles are equal. 

Diagonals bisect one another. 

Rhombus: 

A parallelogram with sides of equal length. 

All the properties of a parallelogram. 

Diagonals are perpendicular to each other. 

Rectangle: 

A parallelogram with a right angle. 

Each of the angles is a right angle. 

Diagonals are equal. 

Square: 

A rectangle with sides of equal length. 

All the properties of a parallelogram, rhombus, and a rectangle. 

Kite: 

A quadrilateral with exactly two pairs of equal consecutive sides.

The diagonals are perpendicular to one another.

One of the diagonals bisects the other.

From figure,

$m\angle B=m\angle D$ but $m\angle A\ne m\angle C$

Trapezium: 

A quadrilateral having exactly one pair of parallel sides. 

Diagonal: 

A simple closed curve is made up of only line segments. 

A line segment connecting two non-consecutive vertices of a polygon is called diagonal.

Convex: 

The measure of each angle is less than ${{180}^{0}}$. 

Concave: 

The measure of at least one angle is more than ${{180}^{0}}$.

Quadrilateral: 

A polygon having four sides. 

Element of quadrilateral: 

(i) Sides: 

Line segments joining the points. 

(ii) Vertices:

Point of intersection of two consecutive sides. 

(iii) Opposite sides:

Two sides of a quadrilateral having no common endpoint. 

(iv) Opposite Angles:

Two angles of a quadrilateral not having a common arm. 

(v) Diagonals:

A line segment is obtained by joining the opposite vertices. 

(vi) Adjacent Angles:

Two angles of a quadrilateral having a common arm. 

(vii) Adjacent Sides:

Two sides of a quadrilateral having a common endpoint.

Download CBSE Class 8 Maths Chapter 3 Notes Free PDF

Continuous revision is one of the most effective techniques for students to overcome their dread of taking final examinations. The CBSE Mathematics Chapter 3 Class 8 Notes from Vedantu include content created by our finest teachers who have taught in the CBSE board. Students will be able to improve their Class 8 test scores by using these review notes. The notes have been made to be simple to grasp. Vedantu's revision notes are available in PDF format for simple download. Students may use the Understanding Quadrilaterals Class 8 Notes PDF to review the whole curriculum and improve their test scores.

Students feel the pressure of taking their final exams. To vanish this pressure, they must revise thoroughly and practice well. By referring to Vedantu’s Class 8 revision notes, students can not only score well, but they can also understand concepts better and enjoy the process of learning instead of cramming last minute. The notes are all easy to understand because they are very simple and to the point.

These Understanding Quadrilaterals Class 8 Notes can be referred to any time once downloaded through the link given. After downloading the Understanding Quadrilaterals Class 8 Notes pdf, students can get their specific doubts cleared or gain further assistance.

About Understanding Quadrilaterals Class 8 Notes

A figure bounded by four line segments such that no three of them are parallel form a quadrilateral.

A quadrilateral has four sides, four vertices, and four angles.

Thus below figure ABCD is a quadrilateral that is bounded by four sides i.e AB, BC, CD, and AD. The four vertices are A, B, C, and D. ∠A, ∠B, ∠C, and ∠D make the four angles of the quadrilateral. And it is written as □ABCD and read as quadrilateral ABCD.

(Image will be uploaded soon)

A line segment drawn from one vertex to the opposite vertex is called the diagonal of the quadrilateral. In the below figure, segment AC and BD are the diagonals of the quadrilateral ABCD.

Terms Related to Quadrilateral

Opposite SIdes: Two sides of a quadrilateral are opposite sides if the sides have no common vertex. In the above figure side AB and DC; Side AD and BC are the two pairs of opposite sides.

Opposite Angles: Two angles of a quadrilateral are opposite angles if they don’t have any common arm. In the above figure, ∠A and  ∠C;  ∠B and ∠D, are two pairs of opposite angles.

Adjacent Sides: Two Sides of a quadrilateral are said to be adjacent if the sides have a common vertex. In the above figure, Side AB and BC; Side BC and CD; Side CD and DA; Side DA and AB are the four pairs of adjacent sides and are also called consecutive sides.

Adjacent Angles: Two angles of a quadrilateral is said to be adjacent angles if the angles have a common side or an arm. In the above figure  ∠A and  ∠B;  ∠B and ∠C, ∠C and  ∠D;  ∠D and ∠A are the four pairs of adjacent angles also called consecutive angles.

Types of Quadrilateral

There are basically six types of quadrilaterals. They are as follows,

Parallelogram: A quadrilateral that has its opposite sides congruent and parallel to each other is a parallelogram. Its opposite angles are also congruent to each other.

Rectangle: A quadrilateral that has its opposite sides equal and all the angles are at right angles(90 0 ) is called a rectangle.

Square: A quadrilateral that has all its four sides equal and opposite sides are parallel, and all the angles at right angles(90 0 ), is called a square.

Rhombus: A quadrilateral has all its sides equal and its diagonals bisect each other at 90 0 is called a rhombus.

Trapezium: A quadrilateral that has only one pair of sides are parallel and the two sides are non-parallel is called a trapezium. The sides may not be equal to each other.

Kite: A quadrilateral that has two pairs of equal adjacent sides and unequal opposite sides is Kite.

Quadrilateral Angles

As we know that a quadrilateral has four angles. The sum of the angles of the quadrilateral is 360 0 .

The sum of all the angles of the □ABCD ∠A +∠B + ∠C + ∠D = 360°.

In the case of square and rectangle, the measure of all the angles is 90 0 .

Therefore we have ∠A = ∠B = ∠C = ∠D = 90°.

Angle Sum Property of Quadrilateral Theorem

The sum of the measures of four angles of a quadrilateral is 360 0

i.e ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.

Benefits of Understanding Quadrilaterals Class 8 Notes By Vedantu  

Understanding Quadrilaterals Class 8 Notes prepared by our experts at Vedantu contain formulae, definitions, diagrams, and quick explanations of the important concepts which make it easier for the school students to grasp the topics easily.

The highlighted notes, easy language and appropriate reference images help students to understand them and remember them easily. Since these notes are prepared by subject experts at Vedantu they give students an edge over their peers when it comes to understanding the theory as well as applications of a concept.

If you haven’t yet downloaded the CBSE Class 8 Maths Revision Notes for Chapter 3 Understanding Quadrilaterals yet, then you’re losing out on the opportunity of studying from the free downloadable expert-curated accurate study material. Further, if you download the free PDF of these Maths revision notes and study them diligently, you will be able to steer your preparation in the right direction with boosted confidence. 

Conclusion 

In conclusion, the Class 8 Revision Notes for CBSE Maths Chapter 3 - Understanding Quadrilaterals provide a valuable resource for students to revise and reinforce their understanding of the topic. These revision notes, available as a free PDF download, cover the important concepts, properties, and characteristics of quadrilaterals in a concise and organized manner. The revision notes begin by introducing the definition of a quadrilateral and its various types, such as parallelograms, rectangles, squares, rhombuses, and trapeziums. Each type is explained with clear explanations and examples, allowing students to grasp the distinguishing features of each quadrilateral.

FAQs on Class 8 Revision Notes for CBSE Maths Chapter 3 Understanding Quadrilaterals (Free PDF Download)

1. When Should You Refer to The Notes?

You should study these revision notes by Vedantu:

Immediately After you Finish a Chapter - Quickly capture the important points, definitions, formulae, theorems and diagrams covered in the chapter and cement them in your mind.

During your Weekly Revisions - Check if you have already forgotten an important point, theorem or formula and revise it once again.

Just before Tests and Exams - To cover the chapter quickly at a glance without spending too much time on the content that is less important.

2. What are the topics covered in Class 8 Chapter 3 Understanding Quadrilaterals?

The topics covered in Class 8 Chapter 3 Understanding Quadrilaterals are Polygons, Classification of Polygons, Diagonals, Convex and Concave Polygons, Regular and Irregular Polygons, Angle Sum Property, Sum of the measures of the Exterior Angles of Polygon, Different kinds of Quadrilateral, Trapezium, Kite, Parallelogram, Elements of a parallelogram, Angles of a parallelogram, Diagonals of a parallelogram, Some Special Parallelograms, Rhombus, A rectangle, and A square.

3. How to gain in-depth knowledge of Chapter 3 of Class 8 Maths? 

The CBSE NCERT questions are answered in the NCERT Solutions for Chapter 3 of Class 8 Maths. The exercise questions are answered in an ideal manner and they best suit the questions from an exam point of view. All questions are prepared by subject matter experts with decades of experience. All these important questions are based on the latest CBSE guidelines, making scheme and syllabus. Referring to these questions will help students get an in-depth understanding of Chapter 3.

4. How to score maximum marks in Chapter 3 of Class 8 Maths examination?

One of the most effective strategies for nervous students to overcome their anxiety about writing final examinations is to revise frequently. They must also practice NCERT’s solved examples and exercises regularly. Mock question papers and questions from different reference books also provide an edge to students and prepares them on a cumulative basis. Vedantu's CBSE Maths Chapter 3 Class 8 Notes contain content provided by our top instructors, all of whom have taught on the CBSE board. Students will be able to get better grades in their Class 8 examinations if they use these revision notes. Understanding Quadrilaterals Class 8 Notes PDF may be downloaded by students to help them review the whole curriculum and improve their test scores. The notes and solutions are free of cost and also available on Vedantu’s website(vedantu.com) and mobile app.

5. What are the benefits of revision notes for Chapter 3 of Class 8 Maths?

Class 8 Understanding Quadrilaterals Formulae, definitions, illustrations, and brief explanations of key ideas are included in the notes created by our specialists at Vedantu, making it easier for school children to comprehend the concepts. Students may readily comprehend and recall the notes because of the highlighted points, simple language, and relevant reference pictures. Because these notes are written by Vedantu topic specialists, students will have an advantage over their classmates when it comes to grasping the theory and applications of a concept.

6. What are the different types of quadrilaterals?

Quadrilaterals are divided into six categories. A parallelogram is a quadrilateral with opposing sides that are congruent and parallel to each other. Its opposing angles are likewise in line with one another. A rectangle is a quadrilateral with opposing equal sides and all angles at right angles (90 degrees). A square is a quadrilateral with all four sides being equal, opposing sides being parallel, and all angles being right angles (90 degrees). A rhombus is a quadrilateral with all of its sides equal and diagonals that bisect each other at 90 degrees. A trapezium is a quadrilateral with only one set of parallel sides and two sides that are not parallel and may or may not be equal. A kite is a quadrilateral with unequal opposed sides and two sets of equal adjacent sides.

7. What are the elements of a quadrilateral?

There are numerous distinct components in a quadrilateral. The line segments that link the vertices are known as sides. Vertices are the intersections of two adjacent sides. A quadrilateral's two opposing sides with no shared termination are referred to as opposite sides. The two quadrilateral angles with no common arm are known as opposite angles. Diagonals are produced by joining the vertices on opposing sides of a line segment. Adjacent Angles are two quadrilateral angles that share a common arm. Adjacent Sides are a pair of quadrilateral sides that share a common termination.

NCERT Solutions

Study materials for class 8.

Extra Questions – Class 8 Maths Chapter 3 Understanding Quadrilaterals

Table of Contents

In Class 8 Mathematics, Chapter 3 focuses on Understanding Quadrilaterals , which are shapes with four sides. To help students practice and understand this chapter better, extra questions have been created. These extra questions are like bonus exercises that give students more practice and help them explore quadrilaterals in more detail.

Fill Out the Form for Expert Academic Guidance!

Please indicate your interest Live Classes Books Test Series Self Learning

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy .

Fill complete details

Target Exam ---

The Class 8 Maths Chapter 3 Extra Questions cover various aspects of quadrilaterals, such as their properties, types, and how they are used. By solving these extra questions, students can improve their knowledge and skills in working with quadrilaterals. The questions also come with solutions, making it easier for students to check their answers and learn from their mistakes.

These extra questions provide a fun and engaging way for students to learn more about quadrilaterals. They can practice identifying different types of quadrilaterals, understanding their features, and solving problems related to them. By working through these extra questions , students can boost their confidence in math and be better prepared for tests and exams.

Class 8 Maths Chapter 3 Extra Questions with Solutions – Understanding Quadrilaterals

For Class 8 students learning about quadrilaterals, extra questions with solutions are a helpful tool. These extra questions from chapter 3 class 8 maths cover different aspects of quadrilaterals and come with answers to check your work. By practicing with these questions, students can improve their understanding of quadrilaterals and how to solve related problems.

The solutions provided not only give the correct answers but also explain how to solve each question step by step. This resource helps students identify areas where they need more practice and enhances their overall grasp of quadrilaterals in a clear and straightforward manner.

Get Extra Questions for Class 8 Maths on Infinity Learn for free.

Enroll now to Online Class 8 Foundation Course

Very Short Answer Type

3x + 5 = 5x – 1

⇒ 3x – 5x = -1 – 5

x + y + z = 360°

(x + 10)° + (3x + 5)° + (2x + 15)° = 180°

⇒ x + 10 + 3x + 5 + 2x + 15 = 180

⇒ 6x + 30 = 180

⇒ 6x = 180 – 30

Question 4. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle.

Solution: The sum of a quadrilateral’s internal angles equals 360°.

Let the quadrilateral’s angles be 2x°, 3x°, 5x°, and 8x°.

2x + 3x + 5x + 8x = 360°

⇒ 18x = 360°

Hence the angles are

2 × 20 = 40°,

3 × 20 = 60°,

5 × 20 = 100°

and 8 × 20 = 160°.

Question 5. Find the measure of an interior angle of a regular polygon of 9 sides.

Solution: Measure of an interior angle of a regular polygon

Question 6. Length and breadth of a rectangular wire are 9 cm and 7 cm respectively. If the wire is bent into a square, find the length of its side.

Side of the square = \(\frac { 32 }{ 4 }\) = 8 cm.

Hence, the length of the side of square = 8 cm.

Then m∠S = 110° (Opposite angles are equal)

Since ∠P and ∠Q are supplementary.

Then m∠P + m∠Q = 180°

⇒ m∠P + 110° = 180°

⇒ m∠P = 180° – 110° = 70°

⇒ m∠P = m∠R = 70° (Opposite angles)

Hence m∠P = 70, m∠R = 70°

and m∠S = 110°

Since the diagonals of a rhombus bisect each other

z = 5 and y = 12

Hence, x = 13 cm, y = 12 cm and z = 5 cm.

⇒ 125° + ∠D = 180°

⇒ ∠D = 180° – 125°

⇒ 125° = y + 56°

⇒ y = 125° – 56°

∠z + ∠y = 180° (Adjacent angles)

⇒ ∠z + 69° = 180°

⇒ ∠z = 180° – 69° = 111°

Hence the angles x = 55°, y = 69° and z = 111°

Now, sum of exterior angles of a polygon is 360°, therefore,

x + 60° + 90° + 90° + 40° = 360°

⇒ x + 280° = 360°

Short Answer Type

3y + 2y – 5 = 180°

⇒ 5y – 5 = 180°

⇒ 5y = 180 + 5°

⇒ 5y = 185°

3y = 3x + 3

⇒ 3 × 37 = 3x + 3

⇒ 111 = 3x + 3

⇒ 111 – 3 = 3x

Hence, x = 36° and y – 37°.

∠ABC = ∠ADC (Opposite angles of a rhombus)

∠ADC = 126°

∠ODC = \(\frac { 1 }{ 2 }\) × ∠ADC (Diagonal of rhombus bisects the respective angles)

⇒ ∠ODC = \(\frac { 1 }{ 2 }\) × 126° = 63°

⇒ ∠DOC = 90° (Diagonals of a rhombus bisect each other at 90°)

∠OCD + ∠ODC + ∠DOC = 180° (Angle sum property)

⇒ ∠OCD + 63° + 90° = 180°

⇒ ∠OCD + 153° = 180°

⇒ ∠OCD = 180° – 153° = 27°

Hence ∠OCD or ∠ACD = 27°

x + 8 = 16 – x

⇒ x + x = 16 – 8

Similarly, OB = OD

5y + 4 = 2y + 13

Hence, x = 4 and y = 3

The Class 8 HOTS Course enhances critical thinking and problem-solving skills through engaging activities and advanced learning techniques, ensuring academic excellence. Class 8 HOTS Course

Question 15. Write true and false against each of the given statements.

(a) Diagonals of a rhombus are equal.

(b) Diagonals of rectangles are equal.

(c) Kite is a parallelogram.

(d) Sum of the interior angles of a triangle is 180°.

(e) A trapezium is a parallelogram.

(f) Sum of all the exterior angles of a polygon is 360°.

(g) Diagonals of a rectangle are perpendicular to each other.

(h) Triangle is possible with angles 60°, 80° and 100°.

(i) In a parallelogram, the opposite sides are equal.

Question 16. The sides AB and CD of a quadrilateral ABCD are extended to points P and Q respectively. Is ∠ADQ + ∠CBP = ∠A + ∠C? Give reason.

Join AC, then

∠CBP + ∠ADQ = ∠BCA + ∠BAC + ∠ACD + ∠DAC

= (∠BCA + ∠ACD) + (∠BAC + ∠DAC)

Higher Order Thinking Skills (HOTS)

Let AD = x cm

diagonal BD = 3x cm

In right-angled triangle DAB,

AD 2 + AB 2 = BD 2 (Using Pythagoras Theorem)

x 2 + AB 2 = (3x) 2

⇒ x 2 + AB 2 = 9x 2

⇒ AB 2 = 9x 2 – x 2

⇒ AB 2 = 8x 2

⇒ AB = √8x = 2√2x

Required ratio of AB : AD = 2√2x : x = 2√2 : 1

Question 18. If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is ∆AMD = ∆CNB? Give reason. (NCERT Exemplar)

AD = BC (opposite sides of parallelogram)

∠AMB = ∠CNB = 90°

∠ADM = ∠NBC (AD || BC and BD is transversal.)

So, ∆AMD = ∆CNB (AAS)

Related content

Get access to free Mock Test and Master Class

Register to Get Free Mock Test and Study Material

Offer Ends in 5:00

Select your Course

Please select class.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Class 8 Maths Chapter 3 Try These Class 8 Maths Exercise 3.1 Solutions Class 8 Maths Exercise 3.2 Solutions Class 8 Maths Exercise 3.3 Solutions Class 8 Maths Exercise 3.4 Solutions

The NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals and Class 8 Maths Chapter 3 Try These Solutions in English and Hindi Medium modified and updated for session 2024-25. As per the revised syllabus, the of exercises in chapter 3 of class 8th Maths are four only, which are given here with solutions.

8th Maths Chapter 3 Solutions in English Medium

• Class 8 Maths Chapter 3 Try These Solutions
• Class 8 Maths Exercise 3.1 in English
• Class 8 Maths Exercise 3.2 in English
• Class 8 Maths Exercise 3.3 in English
• Class 8 Maths Exercise 3.4 in English

8th Maths Chapter 3 Solutions in Hindi Medium

• Class 8 Maths Exercise 3.1 in Hindi
• Class 8 Maths Exercise 3.2 in Hindi
• Class 8 Maths Exercise 3.3 in Hindi
• Class 8 Maths Exercise 3.4 in Hindi
• Class 8 Maths Chapter 3 NCERT Book
• Class 8th Maths Solutions Page
• Class 8 all Subjects Solutions

Class VIII Mathematics chapter 3 is based on latest NCERT Books for current year, useful to all students. Download Prashnavali 3.1, Prashnavali 3.2, Prashnavali 3.3 and Prashnavali 3.4 in Hindi Medium and Exercise 3.1, Exercise 3.2, Exercise 3.3 and Exercise 3.4 in English Medium free to download in PDF format. These NCERT Solutions are applicable for all board using NCERT Books for their academic session. All the solutions are updated on the basis of latest CBSE Curriculum 2024-25. This chapter is based on closed figures like triangles, quadrilaterals and other polygons.

Free NCERT Solutions App for 8th

More about Class 8 Maths Chapter 3

What is a regular polygon state the name of a regular polygon of: (a) 3 sides (b) 4 sides (c) 6 sides.

A regular polygon: A polygon having all sides of equal length and the interior angles of equal size is known as regular polygon. (i) 3 sides Polygon having three sides is called a triangle.

(ii) 4 sides Polygon having four sides is called a quadrilateral.

(iii) 6 sides Polygon having six sides is called a hexagon.

How many sides does a regular polygon have, if the measure of an exterior angle is 24 degree?

Let number of sides be n. Sum of exterior angles of a regular polygon = 360 Number of sides = n = 360/24 = 15 Hence, the regular polygon has 15 sides.

Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.1, Exercise 3.2, Exercise 3.3 and Exercise 3.4 in English Medium as well as Hindi Medium are given below to download in PDF form. Download Class 8 Maths App in English for offline use and Kaksha 8 Ganit App in Hindi Medium for the academic session 2024-25.

In Chapter 3 Understanding Quadrilaterals, we will learn about plane surface and plane figures, different types of polygons like Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon, etc. Number of diagonals in each polygon, a brief description about CONVEX and CONCAVE polygons. Regular and irregular polygons having 3, 4, 5 and 6. Angle sum property of triangle and the questions based on the same fact to find the missing term. Questions based on sum of measure of exterior angles and questions related to Trapezium, Parallelogram, Kite to find the missing side or angle.

Download NCERT Books and Offline apps based on new CBSE Syllabus. Ask your doubts and share your knowledge with your friends and other users.

There are exercises based on the properties of different types of quadrilaterals in this lesson. Just as all the sides and all the angles of the square are equal, the opposite sides of the rectangle are equal, the opposite angle and the diagonal are also equal. Quadrilateral and rectangle have the difference of angles and diagonals. If the diagonals of a rhombus are equal, then it is square. Every angle of a square is a right angle. All the questions in chapter 3 of 8th Maths are mainly based on the properties of polygons.

« Chapter 2: Linear Equations in one Variable

Chapter 4: data handling ».

Copyright 2024 by Tiwari Academy | A step towards Free Education

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals are prepared based on Class 8 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 8 Solutions Maths Chapter 3 are in accordance with the latest CBSE guidelines and marking schemes.

Class 8 Maths Chapter 3 Exercise 3.1 Solutions

Class 8 Maths Chapter 3 Exercise 3.2 Solutions

Class 8 Maths Chapter 3 Exercise 3.3 Solutions

Class 8 Maths Chapter 3 Exercise 3.4 Solutions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Gurukul of Excellence

Classes for Physics, Chemistry and Mathematics by IITians

Join our Telegram Channel for Free PDF Download

Case Study Questions for Class 8 Maths

• Last modified on: 1 year ago
• Reading Time: 7 Minutes

Table of Contents

Here in this article, we are providing case study questions for class 8 maths.

Maths Class 8 Chapter List

Latest chapter list (2023-24).

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Data Handling Chapter 5 Squares and Square Roots Chapter 6 Cubes and Cube Roots Chapter 7 Comparing Quantities Chapter 8 Algebraic Expressions and Identities Chapter 9 Mensuration Chapter 10 Exponents and Powers Chapter 11 Direct and Indirect proportions Chapter 12 Factorisation Chapter 13 Introduction to Graphs

Old Chapter List

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Practical Geometry Chapter 5 Data Handling Chapter 6 Squares and Square Roots Chapter 7 Cubes and Cube Roots Chapter 8 Comparing Quantities Chapter 9 Algebraic Expressions and Identities Chapter 10 Visualising Solid Shapes Chapter 11 Mensuration Chapter 12 Exponents and Powers Chapter 13 Direct and Indirect proportions Chapter 14 Factorisation Chapter 15 Introduction to Graphs Chapter 16 Playing with Numbers

Tips for Answering Case Study Questions for Class 8 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

Download CBSE Books

Exam Special Series:

• Sample Question Paper for CBSE Class 10 Science (for 2024)
• Sample Question Paper for CBSE Class 10 Maths (for 2024)
• CBSE Most Repeated Questions for Class 10 Science Board Exams
• CBSE Important Diagram Based Questions Class 10 Physics Board Exams
• CBSE Important Numericals Class 10 Physics Board Exams
• CBSE Practical Based Questions for Class 10 Science Board Exams
• CBSE Important “Differentiate Between” Based Questions Class 10 Social Science
• Sample Question Papers for CBSE Class 12 Physics (for 2024)
• Sample Question Papers for CBSE Class 12 Chemistry (for 2024)
• Sample Question Papers for CBSE Class 12 Maths (for 2024)
• Sample Question Papers for CBSE Class 12 Biology (for 2024)
• CBSE Important Diagrams & Graphs Asked in Board Exams Class 12 Physics
• Master Organic Conversions CBSE Class 12 Chemistry Board Exams
• CBSE Important Numericals Class 12 Physics Board Exams
• CBSE Important Definitions Class 12 Physics Board Exams
• CBSE Important Laws & Principles Class 12 Physics Board Exams
• 10 Years CBSE Class 12 Chemistry Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Physics Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Maths Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Biology Previous Year-Wise Solved Papers (2023-2024)
• ICSE Important Numericals Class 10 Physics BOARD Exams (215 Numericals)
• ICSE Important Figure Based Questions Class 10 Physics BOARD Exams (230 Questions)
• ICSE Mole Concept and Stoichiometry Numericals Class 10 Chemistry (65 Numericals)
• ICSE Reasoning Based Questions Class 10 Chemistry BOARD Exams (150 Qs)
• ICSE Important Functions and Locations Based Questions Class 10 Biology
• ICSE Reasoning Based Questions Class 10 Biology BOARD Exams (100 Qs)

✨ Join our Online NEET Test Series for 499/- Only for 1 Year

4 thoughts on “ Case Study Questions for Class 8 Maths ”

• Pingback: Case Study Questions for CBSE Class 8 Maths - ebookpublisher.in
• Pingback: Rational Numbers Class 8 Case Study Questions Maths Chapter 1 - XAM CONTENT
• Pingback: Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2 - XAM CONTENT
• Pingback: Square and Square Roots Class 8 Case Study Questions Maths Chapter 5 - XAM CONTENT

Leave a Reply Cancel reply

Editable Study Materials for Your Institute - CBSE, ICSE, State Boards (Maharashtra & Karnataka), JEE, NEET, FOUNDATION, OLYMPIADS, PPTs

Discover more from Gurukul of Excellence

Subscribe now to keep reading and get access to the full archive.

Type your email…

Continue reading

• Class 8 Maths MCQs
• Chapter 3 Understanding Quadrilaterals

Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQs

Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQs   (Questions and Answers) are provided here, online. These objective questions are designed for students, as per the CBSE syllabus (2022-2023) and NCERT guidelines. Solving the chapter-wise questions will help students understand each concept and help to score good marks in exams. Also, learn important questions for class 8 Maths here at BYJU’S.

Practice more and test your skills on Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQs with the given PDF here.

MCQs on Class 8 Understanding Quadrilaterals

Multiple Choice Questions (MCQs) are available for Class 8 Understanding Quadrilaterals chapter. Each problem consists of four multiple options, out of which one is the correct answer. Students have to solve the problem and select the correct answer.

1. Which of the following is not a quadrilateral?

B. Rectangle

C. Triangle

D. Parallelogram

Explanation: A quadrilateral is a four-sided polygon but triangle is a three-sided polygon.

2. Which of the following quadrilaterals has two pairs of adjacent sides equal and its diagonals intersect at 90 degrees?

D. Rectangle

3. Which one of the following is a regular quadrilateral?

B. Trapezium

Explanation: A square has all its sides equal and angles equal to 90 degrees.

4. If AB and CD are two parallel sides of a parallelogram, then:

A. AB>CD

B. AB<CD

D. None of the above

5. The perimeter of a parallelogram whose parallel sides have lengths equal to 12 cm and 7 cm is:

Explanation: Perimeter of parallelogram = 2 (Sum of Parallel sides)

P = 2 (12 + 7)

6. If ∠A and ∠C are two opposite angles of a parallelogram, then:

A. ∠A > ∠C

C. ∠A < ∠C

Explanation: Opposite angles of a parallelogram are always equal.

7. If ∠A and ∠B are two adjacent angles of a parallelogram. If ∠A = 70 ° , then ∠B = ?

Explanation: The adjacent angles of parallelogram are supplementary.

∠A + ∠B = 180°

70° + ∠B = 180°

∠B = 180 – 70° = 110°

8. ABCD is a rectangle and AC & BD are its diagonals. If AC = 10 cm, then BD is:

Explanation: The diagonals of a rectangle are always equal.

9. Each of the angles of a square is:

A. Acute angle

B. Right angle

C. Obtuse angle

D. 180 degrees

Explanation: All the angles of square is at right angle.

10. The quadrilateral whose diagonals are perpendicular to each other is:

A. Parallelogram

C. Trapezium

11. Which of the following is not a regular polygon?

A. Square B. Equilateral triangle C. Rectangle D. Regular hexagon

Answer: C. Rectangle Explanation: A regular polygon is both equiangular and equilateral. But all four sides of a rectangle are not equal, thus it is not a regular polygon.

12. If the two angles of a triangle are 80° and 50°, respectively. Find the measure of the third angle. A. 50° B. 60° C. 70° D. 80°

Answer: A. 50°

Explanation: By the angle sum property of triangle, we know that; Sum of all the angles of a triangle = 180° Let the unknown angle be x 80° + 50° + x = 180° x = 180° – 130° x = 50°

13. In a parallelogram ABCD, angle A and angle B are in the ratio 1:2. Find the angle A. A. 30° B. 45° C. 60° D. 90°

Answer: C.60°

Explanation: As we know, the sum of adjacent angles of a parallelogram is equal to 180° and opposite angles are equal to each other. Thus, in parallelogram ABCD angle A and angle B are adjacent to each other Let angle A = x and angle B = 2x. So, x + 2x = 180° 3x = 180° x = 60°

14. The angles of a quadrilateral are in ratio 1:2:3:4. Which angle has the largest measure? A. 120° B. 144° C. 98° D. 36°

Answer: B.144°

Explanation: Suppose, ABCD is a quadrilateral. Let angle A is x Then, x + 2x + 3x + 4x = 360° [Angle sum property of quadrilateral] 10x = 360° x = 36° Hence, the greatest angle is 4x = 4 x 36 = 144°

15. The length and breadth of a rectangle is 4 cm and 2 cm respectively. Find the perimeter of the rectangle. A. 12 cm B. 6 cm C. 8 cm D. 16 cm

Answer: A. 12 cm Explanation: Given, length of rectangle is 4 cm Breadth of rectangle = 2cm By the formula of perimeter of rectangle, we know that; Perimeter = 2 (Length + Breadth) P = 2(4+2) P = 2 x 6 P = 12 cm

16. The diagonals of a rectangle are 2x + 1 and 3x – 1, respectively. Find the value of x. A. 1 B. 2 C. 3 D. 4

Answer: B.2

Explanation: The diagonals of a rectangle are equal in length. 2x + 1 = 3x -1 1 + 1 = 3x – 2x 2 = x Thus, the value of x is 2.

17. The diagonals of a kite: A. Bisects each other B. Are perpendicular to each other C. Does not bisect each other D. None of the above

Answer: B. Are perpendicular to each other

Explanation: The diagonals of a kite are perpendicular to each other. They intersect at 90 degrees but does not bisect.

18. A rhombus has a side length equal to 5 cm. Find its perimeter. A. 25 B. 10 C. 20 D. 30

Answer: C. 20

Explanation: A rhombus is a parallelogram that has all its four sides equal. Thus, the perimeter of rhombus, P = 4 x side-length P = 4 x 5 P = 20 cm

19. ABCD is a parallelogram. If angle A is equal to 45°, then find the measure of its adjacent angle. A. 135° B. 120° C. 115° D. 180°

Answer: A.135°

Explanation: The adjacent angles of a parallelogram sums up to 180°. Thus, 45° + x = 180° x = 180° – 45° x = 135°

20. The kite has exactly two distinct consecutive pairs of sides of equal length. A. True B. False

Answer: A. True

Explanation: A kite is a quadrilateral that has exactly two distinct consecutive pairs of sides of equal length.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Thank you for help

It is. awesome. 🤞🏻🤞🏻🤞🏻🤞🏻🤞🏻

Hello my name is nishtha

So help full

Nice questions but easy

Thanks for my help

Great,helpful for test

Nice answer

Thanks a lot, it is very useful for exam preparation.

It’s very useful for us thanks alot

Yes it very very useful 😊😊😊😊👍👍👍

It is so helpfull for exam👍

Really it is very useful

Yeah it is very useful for us

It is very useful for me and helpful for my exam.

Vry helpful its really good for practise

Bst objective for brain boosting test

It is very useful for my exam.

Very helpful Thanks a lot ☺☺☺☺

Very useful for exams happening in lockdown

This is helping me in my exams. This is just great 🥰

It’s amazing WOW

This is very helpful to me

This Pdf is very helpfull for me thank you.

Very helpful for my exam preparation. Thank u so much .

Very helpfull😀

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Ncert solutions for class 8 maths chapter 3 understanding quadrilaterals| pdf download.

• Exercise 3.1 Chapter 3 Class 8 Maths NCERT Solutions
• Exercise 3.2 Chapter 3 Class 8 Maths NCERT Solutions
• Exercise 3.3 Chapter 3 Class 8 Maths NCERT Solutions
• Exercise 3.4 Chapter 3 Class 8 Maths NCERT Solutions

NCERT Solutions for Class 8 Maths Chapters:

How many exercises in Chapter 3 Understanding Quadrilaterals

What is equilateral triangle, in a quadrilateral abcd, the angles a, b, c and d are in the ratio 1 : 2 : 3 : 4. find the measure of each angle of the quadrilateral., the interior angle of a regular is 108°. find the number of sides of the polygon., contact form.