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Estimating angles

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In these worksheets, students estimate angles based on the diagrams shown . No protractor is needed.

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Measuring angles

Here you will learn about measuring angles, including how to measure an angle using a protractor.

Students first learn about measuring angles as part of geometry in 4 th grade. They expand that knowledge as they progress through middle school and high school.

What is measuring angles?

Measuring angles is finding the number of degrees an angle is. Angles are measured in degrees using the degree sign ^{\circ} . The tool used for measuring angles is called a protractor .

The degree measure on the top center of a protractor is 90^{\circ} . This is the midpoint of the protractor. Note that the numbers to the left and to the right of the center either go up by ten or go down by ten degrees.

If the angle is acute, you will use the acute measurement (less than 90^{\circ} but greater than 0^{\circ} ), and if the angle is obtuse, you will use the obtuse measurement (greater than 90^{\circ} but less than 180^{\circ} ).

For example, let’s look at the measure of ∠D.

The vertex of the angle, D , is placed on the bottom center of the protractor. One arm of the angle is lined up with the bottom of the protractor at 0^{\circ} . The other arm is used to measure the turn from one arm to the next.

Notice how the arm goes through the measure of 40^{\circ} and 140^{\circ} . Since the angle is obtuse, use the measurement that is greater than 90^{\circ} and less than 180^{\circ} . The angle measure 140^{\circ} .

The angle on a protractor may not always line up with the bottom of the protractor at zero. If this happens, you will subtract in order to find the measurement of the angle.

For example, let’s look at the measure of ∠abc.

Notice how both point A and C are on an angle measure greater than zero. You will have to subtract in order to find the measure of the angle. In order to calculate the correct measure, decide whether to use the top angle measurements or bottom angle measurements.

If using the top angle measurements, notice the arms of the angles read 150^{\circ} and 40^{\circ} . If using the bottom angle measurements, notice the arms of the angles read 140^{\circ} and 30^{\circ} .

To find the measure of the angle, you will subtract the two angle measurements.

150-40=110^{\circ}

140-30=110^{\circ}

The measure of the angle is 110^{\circ} .

[FREE] Angles Check for Understanding Quiz (Grade 4)

Use this quiz to check your grade 4 students’ understanding of angles. 10+ questions with answers covering a range of 4th grade angles topics to identify areas of strength and support!

Common Core State Standards

How does this apply to 4 th grade math and 7 th grade math?

• Grade 4 – Measurement and Data (4.MD.C.6) Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
• Grade 4 – Measurement and Data (4.MD.C.7) Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, example, by using an equation with a symbol for the unknown angle measure.
• Grade 7 – Geometry (7.G.B.5) Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

How to measure angles

In order to measure an angle, you need to:

Determine the type of angle.

Check to make sure the vertex is at the center of the protractor and one side of the angle is lined up with the bottom of the protractor.

Find the degree measure.

Measuring angle examples

Example 1: arm of angle is lined up with zero.

Find the measure of the given angle.

The angle is an acute angle because it appears to be less than 90^{\circ} .

2 Check to make sure the vertex is at the center of the protractor and one side of the angle is lined up with the bottom of the protractor.

The vertex is placed correctly on the protractor. The arm is lined up correctly on the bottom of the protractor.

3 Find the degree measure.

The other arm goes through the 70^{\circ} and 110^{\circ} . Since the angle is acute, the correct measure is 70^{\circ} .

Example 2: arm of angle is lined up with zero

The angle is an obtuse angle because it appears to be greater than 90^{\circ} .

The other arm goes through the 40^{\circ} and 140^{\circ} . Since the angle is obtuse, the correct measure is 140^{\circ} .

Example 3: arm of angle is lined up with zero

The other arm goes through the 75^{\circ} and 105^{\circ} . Since the angle is obtuse, the correct measure is 105^{\circ} .

How to measure angles that are not aligned at zero

In order to measure an angle that is not aligned at zero, you need to:

After deciding which degree measures to use, find the degree measure for each arm.

Subtract the degree measures.

State the number of degrees measured.

Example 4: arm of angle is not lined up with zero

Angle ABC is an obtuse angle because it appears to be greater than 90^{\circ} .

Using the measures that run from left to right, the arm at point A goes through 25^{\circ} , and the arm at point C goes through 160^{\circ} .

Subtract the two measures,

The measure of angle ABC is 135^{\circ} .

Example 5: arm of angle is not lined up with zero

Using the measures that run from left to right, the arm at point A goes through 45^{\circ} , and the arm at point C goes through 90^{\circ} .

State the number of degrees measured

The measure of angle ABC is 45^{\circ} .

Example 6: arm of angle is not lined up with zero

Using the measures that run from left to right, the arm at point A goes through 33^{\circ} , and the arm at point C goes through 119^{\circ} .

The measure of angle ABC is 86^{\circ} .

Teaching tips for measuring angles

• Introduce the protractor by allowing students to use and investigate the tool. Make sure students are comfortable with the different parts of the protractor including the straight edge, the curved edge with degree markings and the midpoint.
• Before jumping into measuring, make sure students are able to identify the different types of angles: acute angle, obtuse angle, right angle, straight angle, and reflex angle.
• While angle worksheets have their place when working with measuring angles, allowing students to have real-world practice using protractors in the classroom is important. Allow students to draw angles and practice measuring the angle using a protractor.

Easy mistakes to make

• Reading the wrong scale when measuring angles A protractor has two different sets of degree markings at the top, one that reads from left to right, and one that reads from right to left. Make sure you have identified the type of angle (acute or obtuse) before deciding which angle markings to read from.

Related angles lessons

• Types of angles
• Acute angle
• Obtuse angle
• Right angle
• Adjacent angles
• Complementary angles
• Supplementary angles
• Geometry theorems
• Vertical angle theorem
• Straight angle
• Angles point
• Pentagon angles

Practice measuring angles questions

1. What is the measure of angle LMN to the nearest degree?

The vertex is placed correctly on the protractor and the arm is lined up correctly on the bottom of the protractor.

The other arm goes through the 150^{\circ} and 30^{\circ} . Since the angle is obtuse, the correct measure is 150^{\circ} .

2. Which angle has a measure closest to 85^{\circ} ?

The angle is an acute angle because 85^{\circ} is less than 90^{\circ} .

These angles are larger than 90 degrees and appear to be obtuse.

This angle is acute, however, the measure is less than 85 degrees.

This angle shows a measure of 85 degrees because the point V is on 0 degrees and point T is on 85 degrees.

3. What is the measure of angle EFG to the nearest degree?

The other arm goes through the 125^{\circ} and 55^{\circ} . Since the angle is acute, the correct measure is 55^{\circ} .

4. Which angle has a measure closest to 115^{\circ} ?

The angle is an obtuse angle because 115^{\circ} is greater than 90^{\circ} .

These angles are smaller than 90 degrees and appear to be acute.

This angle is a straight angle, measuring 180 degrees.

This angle shows a measure of 115 degrees because the point F is on 15 degrees and point D is on 130 degrees. 130-15=115 degrees.

5. What is the measure of angle XYZ to the nearest degree?

The angle is a right angle because it appears to be exactly 90^{\circ} .

Using the measures that run from left to right, the arm at point X goes through 60^{\circ} , and the arm at point C goes through 150^{\circ} .

The measure of angle XYZ is 90^{\circ} .

6. Which angle has a measure closest to 90^{\circ} ?

The angle is a right angle because it is equal to 90^{\circ} .

These angles appear to be acute.

This angle appears to be obtuse.

This angle shows a measure of 90 degrees because point N is on 45 degrees and point P is on 135 degrees. 135-45=90 degrees.

Measuring angles FAQs

A straight angle is an angle that measures 180 degrees. A straight angle and a straight line are the same.

A standard protractor can measure up to a 180 degree angle. To measure an angle over 180 degrees, you can measure the angle in smaller parts, and then subtract the total from 360 degrees.

No, the degrees of an angle can involve both fractions and decimals.

Yes, you are able to measure the angles of different polygons. For example, the sum of the interior angles of a triangle is 180 degrees, and the sum of the interior angles of a quadrilateral is 360 degrees.

The next lessons are

• Angles in parallel lines

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Level 1 Level 2 Level 3 Level 4 Description More Angle Activities

This is level 1; Estimating the size of acute angles. You can earn a trophy if you get at least 9 estimations to within five degrees of the actual size.

This is Estimating Angles level 1. You can also try: Level 2 Level 3 o ">Level 4 Measuring Angles

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Description of Levels

Level 1 - Estimating the size of acute angles

Level 2 - Estimating the size of obtuse angles

Level 3 - Estimating the size of reflex angles

Level 4 - Estimating the size of angles less than 360 o

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Grade 4 - Measurement and Data

Standard 4.MD.C.5b - Practice estimating angles from 5 to 180 degrees.

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An angle that turns through n one-degree angles is said to have an angle measure of n degrees

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How to Estimate Angle Measurements

Estimating angle measurements is a useful skill for students to develop, as it helps them gain a better understanding of angles and their properties.

A Step-by-step Guide to Estimating Angle Measurements

Here’s a step-by-step guide to help students estimate angle measurements:

Step 1: Understand the Basics of Angles

An angle is formed by two rays that have a common endpoint, called the vertex. Angles are usually measured in degrees (°). There are three main types of angles to consider:

• Acute angles: These are angles that are less than \(90^°\).
• Right angles: These are angles that are exactly \(90^°\).
• Obtuse angles: These are angles that are greater than \(90^°\) but less than \(180^°\).

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Step 2: identify reference angles.

To estimate angle measurements, it’s helpful to have some reference angles in mind. Here are a few common angles to remember:

• \(45^°\): This angle is half of a right angle and is often found in squares or rectangles that have been divided diagonally.
• \(60^°\) and \(30^°\): These angles are often found in equilateral triangles, where all angles are equal to \(60^°\). A \(30^°\) angle can be found in a right-angled triangle with one angle of \(60^°\) and another of \(90^°\).
• \(90^°\): A right angle, often found in squares, rectangles, and right-angled triangles.
• \(180^°\): A straight angle or a straight line.

Step 3: Observe the Given Angle

Take a close look at the angle you need to estimate. Compare it to the reference angles you learned in Step 2.

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Step 4: compare and estimate.

Now, compare the given angle to your reference angles. Use your understanding of the basic angle types (acute, right, and obtuse) to help you make an educated guess.

For example:

• If the angle appears smaller than a right angle (\(90^°\)), it’s an acute angle.
• If the angle appears to be exactly half of a right angle, you can estimate it as \(45^°\).
• If the angle seems larger than a right angle but smaller than a straight angle (\(180^°\)), it’s an obtuse angle.

Step 5: Practice and Improve

Estimating angles takes practice. Try estimating angles in your daily life, such as when looking at the hands of a clock or noticing the angles in various shapes and objects. The more you practice, the better you’ll become at estimating angles.

Remember that estimating angle measurements is a useful skill, but it may not be as precise as using a protractor or other measuring tools. It’s a great way to develop an intuitive understanding of angles and their properties.

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Measuring Angles Using a Protractor Worksheets

Angles are an important concept in geometry, and hence it becomes vital for grade 4 and grade 5 children to learn to measure them. The size of the angle is the turn from one arm of the angle to the other, and to measure this, we require a protractor that comes with an outer and an inner scale. Bolster practice in measuring angles using a protractor starting with 5-degree increments and moving to a single-degree increments, measuring reflex angles, solving for x and much more. Begin your practice with our free sample worksheets and subscribe for the entire collection.

Measuring Angles with 5-Degree Increments | Inner Scale

Is the angle between the two rays with a common vertex 40° or 60°? Learn the ropes of using the inner scale of a protractor to measure angles with 5° increments.

• Download the set

Measuring Angles using the Protractor | Inner Scale

Place the midpoint of the protractor on the vertex, line up one arm with the base line of the protractor, measure the angles with 1-degree increments using the inner scale in these pdfs on measuring angles.

Measuring Reflex Angles

Angles that measure more than 180°, but less than 360° are reflex angles. Encourage students to determine the size of each reflex angle using the protractor in this set of measuring reflex angles worksheets.

Measuring Angles with 5-Degree Increments | Inner & Outer Scale

Angles can be measured using the inner or outer scale of the protractor. Direct students to use the inner scale if the angle opens to the right, and the outer scale if the angle opens to the left, so they can easily measure the angles.

Measuring Angles | Inner & Outer Scale

Utilize this batch of printable exercises on measuring angles for children to practice using both the inner and outer scales, while determining the size of the angles with 1-degree increments.

Measuring and Classifying Angles

First, measure the angles using your protractor, and then classify them as acute, obtuse, right, straight, or reflex angle.

Measuring and Ordering Angles | Puzzles

Exercise the brains of your 4th grade children as they measure each angle, arrange the angles based on the size, and decode the names of the animals in these measuring and ordering angles puzzle worksheets.

Measuring Angles and Finding x

Get kids to measure the angle first, and then equate the expression to the size of the angle, followed by isolating x, making it the subject, and solving the expression in these pdfs on measuring angles and finding x.

Measuring Angles Revision

Offered in these pdf measuring angles revision worksheets is a blend of rays, shapes, and clocks. Check for yourself how well your 4th grade and 5th grade learners can measure angles in this variety of exercises.

Related Worksheets

» Acute, Right, and Obtuse Angles

» Reading Protractors

» Drawing Angles

» Estimating Angles

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Measuring Angles

Measuring angles is done by using a simple geometric tool such as a protractor. A protractor is used more often than a compass. Measuring angles is useful in knowing at what measure the angle is exactly. In geometry, there are different types of angles that we encounter in our daily life and by using these tools we can find out the measurement of angles . Let us see how to measure an angle, the steps required, and solve a few examples.

What is Measuring Angles?

Measuring angles is done by using basic geometric tools like a protractor and a compass. These tools help in finding the exact measure of an angle. A protractor helps in providing the exact measure of the angle and a compass helps in constructing the angle. Measuring angles is done in three ways - degrees, radians, and revolution. Let us see what these three ways of measuring angles are.

Degree is the unit of measure of an angle and is measured by using the geometric tool - a protractor. A degree is denoted by the symbol '°'. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts. The different angles with different degrees are 30°, 45°, 90°, and so on. And is read as 30 degrees, 45 degrees, 90 degrees, etc.

Radian is another unit of measurement of an angle and is used in place of degrees when the angle needs to be measured in terms of radians. By definition, a radian is the ratio of the length of the arc that the angle subtends of a circle, divided by the length of the radius of the same circle. In other words, a radian is an angle subtended by the arc of the length of the radius of the same circle at the center and the ratio will give the radian measure of the angle. Radian is denoted as rad or c and is written as 1.7 radians or 1.7 rad or 1.7 c . Half a circle is 180° which is π radian and one complete revolution is 2π radian.

Revolution is the simplest form of measuring angles. Along degrees, the revolution also is the unit of 360° as an angle is basically a subdivision of a circle rather than the sum of a few degrees. For example, while measuring in the revolution we can say a right angle is a quarter of a circle while in degrees an angle is read as a right angle is 90°.

Measurement of Angles Using Protractor

An angle is measured by using two geometric tools - a protractor and a compass. While a protractor can be used for both constructing and measuring, a compass is mostly used for constructing an angle. A protractor is considered one of the most important geometric tools as it helps in measuring angles in both degrees and radians. When we look at a protractor we can see measurements from 0 to 180 from left to right at the outer edge and 180 to 0 from right to left on the inner edge. The measurements in both the edges total up to 180°.

While measuring through a protractor the measure is usually in degrees. If the angle is on the left side of the protractor, we use the outer edge measurement and if the angle is on the right side of the protractor, we use the inner edge measurements. The steps to measure an angle are:

• Step 1: Place the center of the protractor on the vertex of the angle.
• Step 2: Superimpose one side of the angle with the zero line of the protractor.
• Step 3: The angle is equal to the number of degrees crossed on the protractor.

Let us look at an example. Measure ∠AOB.

Step 1: Align the protractor with the ray OB as shown below. Start reading from the 0° mark on the bottom-right of the protractor.

Step 2: The number on the protractor that coincides with the second ray is the measure of the angle. Measure the angle using the number on the lower arc of the protractor.

Therefore, ∠AOB = 60° . Since the measure is greater than 0° and lesser than 90°, we can say that ∠AOB is an acute angle .

Example: Using the same example as above, let us measure the angle from the other side of the protractor. Measure ∠AOC.

Step 1: Align the protractor with the ray CO as shown below. Start reading from the 0° mark on the bottom-left of the protractor.

Step 2: The number on the protractor that coincides with the second ray is the measure of the angle. Measure the angle using the number on the top arc of the protractor.

Therefore, ∠AOC = 120°. Since the measure is greater than 90° and lesser than 180°, we can say that ∠AOC is an obtuse angle .

Constructing and Measuring Angles Using Protractor

A protractor can be used not only for measuring but also for constructing angles. This helps in both measuring the angles accurately and learning how to use the protractor. Let us see how to draw 40° using a protractor.

• Draw a baseline AB.
• Mark the point O and place the center of the protractor at O.
• Align the baseline of the protractor with the line OB.
• In the inner readings, look for 40º and mark it as point C.
• Now using a scale, join O and C.

To measure 230º, a reflex angle, we can write it as 180° + 50°. We can just flip the protractor along the baseline and then mark 50°. 180° + 50° = 230°

Units of Measurement of Angles

The angles in geometry can be measured using mainly two units:

Radians is the SI unit of measuring angles and is most commonly used in the concept of trigonometry. Another unit that is used for the measurement of angles is degrees, denoted by °, is commonly used in geometry. One revolution is equal to 360 degrees or 2π radians.

Important Notes on Measurement of Angles

• Measurement of angles is done by using basic geometric tools like a protractor and a compass.

The angles in geometry can be measured using mainly two units - radians and degrees.

Related Articles

• 180 Degree Angle
• Central Angle
• Supplementary Angles
• Radian to Degrees

Measuring Angles Examples

Example 1: In triangle ABC, use a protractor and measure ∠CAB.

Place the protractor baseline along the line AB and the center of the protractor at vertex A. Observe the reading in the protractor which overlaps with line AC.

Answer: Therefore, ∠CAB = 60°

Example 2: What is the angle formed at vertex B of the square ABCD?

Place the protractor center at vertex B of the square and observe the reading.

Answer: ∠B = 90°

Example 3: Help Ben find the measurement of ∠ABC by looking at the image below.

Solution: By looking at the image, we can see that the ray AB is crossing the protractor at 153°. Therefore, ∠ABC = 153°.

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Measurement of Angles Questions

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FAQs on Measuring Angles

What is meant by measuring angles.

In geometry, the process of reading angles or finding out the exact angle is called measuring angles . The best way to measure angles is by using the geometric tool known as the protractor. It is a semicircular instrument with markings from 0° to 180°.

What are the 3 Ways of Measurement of Angles?

In geometry, the 3 ways or units to measure angles are degree, radians, and revolution.

• Degree: The most common way to measure angles is degrees. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts.
• Radians: A radian is an angle subtended by the arc of the length of the radius of the same circle at the center and the ratio will give the radian measure of the angle.
• Revolution: A revolution is the measure of the angle when it rotates one side completing a 360°.

What is the Best Way of Measuring Angles?

The best way measuring angles is by using a protractor. The steps are:

• Place the center of the protractor on the vertex of the angle.
• Superimpose one side of the angle with the zero line of the protractor.
• The angle is equal to the number of degrees crossed on the protractor.

How Do You Measure an Angle Without a Protractor?

To measure an angle without using a protractor, we use a simple ruler. We first connect the two rays at a point creating a triangle. Here are the steps:

• Draw a line connecting the two rays of the angle.
• Measure the length of the base of the triangle using a ruler. Also called as run.
• Measure the length of the straight side of the triangle using a ruler. Also called as rise.
• Once both the lengths are obtained we use a simple slope formula i.e. Slope = Rise/Run.
• Type the value for slope into a scientific calculator, then press the inverse tan button.

What are the Different Measures of Angles?

The different measures or types of angles are:

• Acute Angle: Measure between 0° to 90°.
• Obtuse Angle: Measure between 90° to 180°
• Right Angle: Measure is exactly 90°.
• Straight Angle: Measure is exactly 180°.
• Reflex Angle: Measure between 180° to 360°.
• Complete or Full Angle: Measure is exactly 360°.

Which Instrument is Used for Measurement of Angles?

The most commonly used instrument that is used for the measurement of angles is the protractor. A protractor is considered to be an important measuring instrument that is in the shape of a semi-circle.

What are the Units Used for Measuring Angles?