How to construct a 150 degree angle

How to Construct a 150 Degree Angle is a simple geometry topic for students. How to Construct a 150 Degree Angle helps us to draw an exact 150 Degree Angle using easy steps and basic tools. This topic is important because it builds a strong base in maths and improves drawing skills.

Table of Contents

• What Is a 150 Degree Angle?
• Instruments Required to Construct a 150 Degree Angle
• How to Construct a 150 Degree Angle Step by Step
• Constructing Related Angles From 150° Angle
• Practice Questions on Constructing a 150 Degree Angle
• Frequently Asked Questions on construct a 150 degree angle

What Is a 150 Degree Angle?

A 150 degree angle is an obtuse angle that measures exactly 150°. It is 60° more than a right angle (90°) and 30° less than a straight angle (180°). It can be constructed by forming a 30° angle and using its supplementary angle, or by combining a 120° angle and a 30° angle.

Instruments Required to Construct a 150 Degree Angle

• A pencil

• A ruler or straightedge (for drawing straight lines only)

• A pair of compasses that can hold its width steady

How to Construct a 150 Degree Angle Step by Step

Step 1: Draw a ray OC.

Step 2: With O as the vertex, construct a 60° angle by drawing ray OB using a compass and ruler.

Step 3: Bisect the 90° angle between OB and the extension of OC to form a 45° angle. Then draw ray OA through the point where the angle bisector passes so that it lies 150° from ray OC.

Step 4: The angle formed between OA and OC is 150°. Therefore, ∠AOC = 150°, which is the required angle.

Constructing Related Angles From 150° Angle

Once you know how to construct a 150° angle, you can use it to create several other common angles.

• 75°: Bisect the 150° angle. Half of 150° is 75°.

• 30°: Construct a 60° angle, then bisect it. Half of 60° is 30°.

• 60°: Construct a 60° angle directly using a compass and ruler.

• 120°: Construct two adjacent 60° angles. Together they form 120°.

• 180°: Extend the base ray to form a straight angle.

• 210° (Reflex Angle): Measure the remaining angle around the point. Since a full angle is 360°, the reflex angle is 360° − 150° = 210°.

Practice Questions on Constructing a 150 Degree Angle

Test your understanding of constructing a 150° angle with these practice questions.

1. Which angle is commonly constructed first before creating a 150° angle?

2. Draw a ray OC and construct a 150° angle at point O using only a ruler and compass.

3. What type of angle is a 150° angle?

4. What is the measure of the supplementary angle of 150°?

5. Which geometric construction is used to obtain a 30° angle while constructing a 150° angle?

6. True or False: A 150° angle is greater than a right angle but less than a straight angle.

7. Which of the following methods can be used to construct a 150° angle?

• a) 90° + 30°

• b) 120° + 30°

• c) 180° − 30°

• d) Both b and c

8. If you subtract 30° from 180°, what angle is formed?

9. Which tool is used to divide a 60° angle into two equal angles?

10. Explain why constructing a 30° angle is important when constructing a 150° angle.

Answers

1. 60° angle

2. Draw ray OC, construct a 60° angle, bisect it to obtain 30°, and use the supplementary angle to form 150°.

3. Obtuse angle

4. 30°

5. Angle bisector

6. True

7. d) Both b and c

8. 150°

9. Compass and angle bisector

10. A 150° angle can be constructed by subtracting a 30° angle from a straight angle (180°). Therefore, constructing a 30° angle is an essential step in the construction.