Angles Questions

Angles questions and answers are available here to help students understand how to solve basic angles problems. These questions cover the different types of angles and their measures, and finding the missing angles when a pair or more than two angles are given in a specific relation. You will also get some extra practice questions at the end of the page. These will help you to improve your geometry skills and get a clear understanding of angles.

What are angles?

In geometry, angles are the figures formed by two rays that are connected by a common point called the vertex. We can measure the angles between two lines, rays or line segments using one of the geometric tools called a protractor. Based on the measure of these angles, we can classify them.

The different types of angles are listed below:

• Acute angle (< 90°)
• Obtuse angle (> 90° and < 180°)
• Right angle (= 90°)
• Straight angle (= 180°)
• Reflex angle (> 180° and < 360°)
• Full rotation angle (= 360°)

Also, check: Angles

Angles Questions and Answers

1. Classify the following angles:

(i) 55°

(ii) 146°

(iii) 90°

(iv) 250°

Solution:

(i) 55°

55° < 90°

Thus, 55° is an acute angle.

(ii) 146°

90° < 146° < 180°

So, 146° is an obtuse angle.

(iii) 90°

90° is a right angle.

(iv) 250°

180° < 250° < 360°

Thus, 250° is a reflex angle.

2. Write two examples of obtuse angles and reflex angles.

Solution:

As we know, obtuse angles are the angles that measure less than 180° and greater than 90°.

Examples: 112°, 177°

Reflex angles measure less than 360° and greater than 180°.

Examples: 210°, 300°

3. Find the measure of an angle which is complementary to 33°.

Solution:

If the sum of two angles is 90°, they are called complementary angles.

Let x be the angle which is complementary to 33°.

So, x + 33° = 90°

x = 90° – 33° = 57°

Therefore, the required angle is 57°.

4. What is the measure of an angle that is supplementary to 137°?

Solution:

If the sum of two angles is 180°, they are called supplementary angles.

Let x be the angle which is supplementary to 137°.

So, x + 137° = 180°

x = 180° – 137° = 43°

Hence, the required angle is 43°.

5. If three angles 2x, 3x, and x together form a straight angle, find the angles.
Solution:

We know that straight angle = 180°

Given that the angles 2x, 3x, and x form a straight angle.

That means 2x + 3x + x = 180°

6x = 180°

x = 180°/6

x = 30°

2x = 2 × 30° = 60°

3x = 3 × 30° = 90°

Therefore, the angles are 60°, 90° and 30°.

6. Are 125° and 65° supplementary angles?

Solution:

As we know, the condition for supplementary angles is that they add up to 180°.

Given angles: 125°, 65°

Sum = 125° + 65° = 190°

Thus, 125° and 65° are not supplementary angles.

7. What is the measure of a complete angle?

Solution:

The measure of a complete angle is 360°.

Two straight angles form a complete angle, i.e., 180° + 180° = 360°.

Four right angles form a complete angle, i.e., 90° + 90° + 90° + 90° = 360°.

8. Find the value of y if (4y + 22)° and (8y – 10)° form a linear pair.

Solution:

According to the given,

(4y + 22)° + (8y – 10)° = 180°

4y + 22° + 8y – 10° = 180°

12y + 12° = 180°

12y = 180° – 12°

12y = 168°

y = 168°/12

y = 14°

9. Three angles at a point are 135°, 75° and x. Find the value of x.

Solution:

Given angles at a point are: 135°, 75°, x

As we know, the sum of angles at a point = 360°

So, 135° + 75° + x = 360°

210° + x = 360°

x = 360° – 210° = 150°

Therefore, the value of x is 150°.

10. If 3x + 24° and 5x – 16° are congruent, then find the value of x.

Solution:

Congruent angles mean equal angles.

So, 3x + 24° = 5x – 16°

⇒ 5x – 3x = 24° + 16°

⇒ 2x = 40°

⇒ x = 40°/2

⇒ x = 20°

Thus, the value of x is 20°.

Practice Problems on Angles

1. Are 42° and 58° complementary angles?
2. How do you find the measure of an angle which is supplementary to 92°?
3. What is the condition for a reflex angle?
4. If 38° and 2x + 26° form a right angle, find the value of x.
5. Classify the following angles:
   
   (i) 72°

(ii) 127°

(iii) 180°

(iv) 315°