Degree Measurement: Complete Concept, Short Notes, MCQs & Practice Worksheet

Degree measurement is a method used to measure the size of an angle. It tells us how much an angle has opened between its two arms. The unit used for measuring angles in this method is called a degree, represented by the symbol °.

• A small angle may measure 30°.
• A right angle measures 90°.
• A straight angle measures 180°.
• A complete angle measures 360°.

Degree measurement is one of the most important concepts in geometry and is widely used in school mathematics.

What Is a Degree?

A degree is a unit used to measure an angle.

A complete rotation around a fixed point is divided into 360 equal parts. Each part is called one degree.

Therefore:

1 complete angle = 360°

This means that if an object makes one complete turn, it rotates through an angle of 360 degrees.

For example, half of a complete rotation is:

360° ÷ 2 = 180°

Therefore, a straight angle measures 180°.

What Is Degree Measure?

The numerical value assigned to an angle is called its degree measure.

For example, if an angle is written as 45°, its degree measure is 45 degrees.

Similarly:

• 30° has a degree measure of 30°.
• 60° has a degree measure of 60°.
• 90° has a degree measure of 90°.
• 120° has a degree measure of 120°.
• 180° has a degree measure of 180°.

The symbol ° is written after the numerical value to indicate that the measurement is in degrees.

How to Measure Degrees of an Angle?

A protractor is commonly used to measure angles in degrees.

To measure an angle using a protractor, follow these steps:

1. Place the center of the protractor exactly on the vertex of the angle.
2. Align the baseline of the protractor with one arm of the angle.
3. Identify the point where the other arm crosses the scale of the protractor.
4. Read the correct scale, starting from the 0° mark on the aligned arm.
5. Write the measurement with the degree symbol (°).

For example, if the second arm passes through the 60° mark, the angle measures 60°.

Types of Angles According to Degree Measurement

Angles can be classified according to their degree measure.

1. Zero Angle

An angle measuring 0° is called a zero angle.

Degree measure = 0°

Its two arms lie on top of each other.

2. Acute Angle

An angle greater than 0° but less than 90° is called an acute angle.

Examples:

20°, 35°, 45°, 60°, 75°

Thus:

0° < Acute angle < 90°

3. Right Angle

An angle measuring exactly 90° is called a right angle.

Degree measurement = 90°

A right angle is usually represented by a small square at its vertex.

Examples of right angles can be seen at the corners of a square or rectangle.

4. Obtuse Angle

An angle greater than 90° but less than 180° is called an obtuse angle.

Examples:

100°, 120°, 135°, 150°

Thus:

90° < Obtuse angle < 180°

5. Straight Angle

An angle measuring exactly 180° is called a straight angle.

Degree measurement = 180°

Its two arms form a straight line.

6. Reflex Angle

An angle greater than 180° but less than 360° is called a reflex angle.

Examples:

200°, 225°, 270°, 300°

Thus:

180° < Reflex angle < 360°

7. Complete Angle

An angle measuring exactly 360° is called a complete angle.

Degree measurement = 360°

It represents one complete rotation around a point.

Degree Measurement of a 90 Degree Angle

A 90 degree angle is called a right angle.

It is one of the most important angles in geometry.

For example:

90° = Right angle

A right angle can be found in:

• Corners of a book
• Corners of a rectangular table
• Corners of a square
• Many buildings and structures
• The meeting of perpendicular lines

Two lines are perpendicular when they intersect to form angles of 90°.

Important Degree Measurements to Remember

Some common angle measurements are:

Type of Angle	Degree Measure
Zero angle	0°
Acute angle	Between 0° and 90°
Right angle	90°
Obtuse angle	Between 90° and 180°
Straight angle	180°
Reflex angle	Between 180° and 360°
Complete angle	360°

Examples of Degree Measurement

Example 1

Classify an angle measuring 45°.

Since 45° is greater than 0° and less than 90°, it is an acute angle.

Answer: Acute angle

Example 2

Classify an angle measuring 90°.

Since the angle measures exactly 90°, it is a right angle.

Answer: Right angle

Example 3

Classify an angle measuring 135°.

Since 135° is greater than 90° and less than 180°, it is an obtuse angle.

Answer: Obtuse angle

Example 4

Classify an angle measuring 180°.

An angle measuring 180° is a straight angle.

Answer: Straight angle

Example 5

Classify an angle measuring 270°.

Since 270° is greater than 180° and less than 360°, it is a reflex angle.

Answer: Reflex angle

Relationship Between Common Angles

A few important relationships are useful for solving geometry problems.

A straight angle is:

180° = 2 × 90°

A complete angle is:

360° = 2 × 180°

A complete angle is also:

360° = 4 × 90°

Therefore, four right angles make one complete angle.

Why Is Degree Measurement Important?

Degree measurement is important because it allows us to describe and compare angles accurately.

It is used in:

• Geometry
• Construction
• Engineering
• Architecture
• Navigation
• Design
• Maps
• Mathematics
• Everyday measurements

Understanding degree measurement also helps students learn more advanced topics such as triangles, quadrilaterals, circles, trigonometry, and angles in standard position.

Common Mistakes in Degree Measurement

Students should avoid the following mistakes when measuring angles:

1. Reading the wrong scale

A protractor usually has two scales. Always start from the 0° mark on the arm that has been aligned with the baseline.

2. Placing the center incorrectly

The center of the protractor must be placed exactly at the vertex of the angle.

3. Confusing 90° and 180°

A 90° angle is a right angle, while a 180° angle is a straight angle.

4. Forgetting the degree symbol

An angle measurement should normally be written with the degree symbol, such as 60°.

Quick Revision

• Degree (°) is a unit for measuring angles.
• One complete rotation is 360°.
• A right angle measures 90°.
• A straight angle measures 180°.
• A complete angle measures 360°.
• An acute angle is between 0° and 90°.
• An obtuse angle is between 90° and 180°.
• A reflex angle is between 180° and 360°.
• A protractor is used to measure angles in degrees.
• The numerical value of an angle in degrees is called its degree measure.

Short Notes on Degree Measurement

Degree Measurement:
A method of measuring the size of an angle in degrees is called degree measurement.

Degree:
A degree is a unit of angle measurement and is represented by °.

Complete Angle:
One complete rotation measures 360°.

Right Angle:
An angle measuring 90° is called a right angle.

Straight Angle:
An angle measuring 180° is called a straight angle.

Acute Angle:
An angle greater than 0° and less than 90° is called an acute angle.

Obtuse Angle:
An angle greater than 90° and less than 180° is called an obtuse angle.

Reflex Angle:
An angle greater than 180° and less than 360° is called a reflex angle.

Protractor:
A protractor is a mathematical instrument used to measure and draw angles.

Important fact:
360° = 4 × 90° = 2 × 180°

MCQs on Degree Measurement

1. What is the unit used to measure an angle?

A. Meter
B. Degree
C. Kilogram
D. Liter

Answer: B. Degree

2. What is the symbol for degree?

A. #
B. %
C. °
D. +

Answer: C. °

3. What is the degree measure of a right angle?

A. 45°
B. 60°
C. 90°
D. 180°

Answer: C. 90°

4. What is the degree measure of a straight angle?

A. 90°
B. 120°
C. 180°
D. 360°

Answer: C. 180°

5. What is the measure of a complete angle?

A. 90°
B. 180°
C. 270°
D. 360°

Answer: D. 360°

6. Which instrument is commonly used to measure an angle?

A. Ruler
B. Compass
C. Protractor
D. Calculator

Answer: C. Protractor

7. An angle measuring 45° is:

A. Acute
B. Right
C. Obtuse
D. Straight

Answer: A. Acute

8. An angle measuring 120° is:

A. Acute
B. Right
C. Obtuse
D. Straight

Answer: C. Obtuse

9. An angle measuring 270° is:

A. Acute
B. Obtuse
C. Straight
D. Reflex

Answer: D. Reflex

10. How many degrees are there in one complete rotation?

A. 90°
B. 180°
C. 270°
D. 360°

Answer: D. 360°

11. Which of the following is an acute angle?

A. 30°
B. 90°
C. 120°
D. 180°

Answer: A. 30°

12. Which angle is exactly half of a complete angle?

A. 45°
B. 90°
C. 180°
D. 270°

Answer: C. 180°

Worksheet / Assignment on Degree Measurement

Name: ____________________

Class: ____________________

Date: ____________________

Part A: Fill in the Blanks

1. The unit used to measure an angle is called a __________.
2. The symbol for degree is __________.
3. A right angle measures __________.
4. A straight angle measures __________.
5. A complete angle measures __________.
6. An angle less than 90° and greater than 0° is called an __________ angle.
7. An angle greater than 90° and less than 180° is called an __________ angle.
8. An angle greater than 180° and less than 360° is called a __________ angle.
9. A __________ is used to measure angles.
10. Four right angles make a __________ angle.

Part B: Classify the Angles

Classify each angle as acute, right, obtuse, straight, reflex, or complete.

1. 25° = __________
2. 90° = __________
3. 110° = __________
4. 180° = __________
5. 225° = __________
6. 360° = __________
7. 75° = __________
8. 150° = __________

Part C: Answer the Questions

1. What is degree measurement?
2. Define one degree.
3. What is a right angle?
4. What is the degree measure of a straight angle?
5. What is the difference between an acute angle and an obtuse angle?
6. What instrument is used to measure an angle?
7. How many degrees are there in one complete rotation?
8. Why must we select the correct scale when using a protractor?

Part D: Practice

1. A complete angle is divided into four equal angles. Find the measure of each angle.
2. Two right angles are placed together. What is their total degree measure?
3. An angle measures 65°. Classify it.
4. An angle measures 145°. Classify it.
5. An angle measures 250°. Classify it.

Conclusion

Degree measurement provides a simple and accurate way to measure angles. By understanding degrees and the different types of angles, students can easily identify and compare angles in geometry.

Remember these three important measurements:

Right angle = 90°

Straight angle = 180°

Complete angle = 360°

For more mathematics notes, recorded lectures, assessments, lesson plans, and other useful learning resources, visit Nisar Math Academy at nisarmathacademy.com. Students can access selected free resources, while full course content is available through website membership.

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