How to construct a 135 degree angle

How to Construct a 135 Degree Angle is a simple geometry topic for students. How To Construct a 135 Degree Angle helps us to draw an exact 135 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 135 Degree Angle?
• Instruments Required to Construct a 135 Degree Angle
• How to Construct a 135 Degree Angle Step by Step
• Constructing Related Angles From 135 Degree
• Practice Questions on Construct a 135 Degree Angle
• Frequently Asked Questions on Construct a 135 Degree Angle

What Is a 135 Degree Angle?

A 135 degree angle is an obtuse angle that measures exactly 135°. It is 45° more than a right angle (90°) and 45° less than a straight angle (180°). It can be constructed by combining a 90° angle and a 45° angle.

Instruments Required to Construct a 135 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 135 Degree Angle Step by Step

Step 1: Draw a ray BA.

Step 2: With B as the vertex, construct a 90° angle by drawing a perpendicular ray BG to BA.

Step 3: Using the same compass width, construct a 45° angle between BG and the extension of BA by bisecting the 90° angle on the left side. Draw the ray BH through the point where the angle bisector passes.

Step 4: The angle formed between BA and BH is 135°. Therefore, ∠ABH = 135°, which is the required angle.

Constructing Related Angles From 135 Degree

Once you know how to construct a 135° angle, you can use it to create several other common angles.

• 45°: Bisect a 90° angle. Half of 90° is 45°.

• 90°: Construct a perpendicular line to form a right angle.

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

• 67.5°: Bisect the 135° angle. Half of 135° is 67.5°.

• 225° (Reflex Angle): Measure the remaining angle around the point. Since a full angle is 360°, the reflex angle is 360° − 135° = 225°.

Practice Questions on Construct a 135 Degree Angle

1. Which two angles are commonly used to construct a 135° angle?
2. Draw a ray BA and construct a 135° angle at point B using only a ruler and compass.
3. What type of angle is a 135° angle?
4. If you add a 90° angle and a 45° angle, what angle do you get?
5. Which construction is needed to obtain a 45° angle while constructing a 135° angle?
6. True or False: A 135° angle is greater than a right angle but less than a straight angle.
7. Which of the following constructions results in a 135° angle?
   • a) 60° + 30°
   • b) 90° + 45°
   • c) 45° + 45°
   • d) 60° + 60°
8. If you subtract 45° from 180°, what angle is formed?
9. Which tool is used to divide a 90° angle into two equal angles?
10. Explain why constructing a 45° angle is important when constructing a 135° angle.

Answers:

1. 90° and 45°
2. Draw ray BA, construct a 90° angle at B, then construct a 45° angle adjacent to it to obtain a 135° angle.
3. Obtuse angle
4. 135°
5. Bisecting a 90° angle
6. True
7. b) 90° + 45°
8. 135°
9. Angle bisector
10. A 135° angle is formed by combining a 90° angle with a 45° angle, so constructing a 45° angle is an essential step in the construction.