📐 Angles — Grade 5

Learn all about angles — from tiny acute angles to full turns! You will measure, calculate and find missing angles.

1. Types of Angles

Acute

Less than 90°

Right Angle

Exactly 90°

Obtuse

90° – 180°

Straight Line

Exactly 180°

Reflex

180° – 360°

Full Turn

Exactly 360°

A right angle is shown with a small square in the corner. Protractors help us measure angles precisely.

2. Measuring and Drawing Angles

To measure an angle with a protractor:

Place the centre of the protractor on the vertex (corner) of the angle.
Line up one arm of the angle with the 0° line.
Read the scale where the other arm crosses. Use the inner scale if the angle opens to the right; the outer scale if it opens to the left.
Check your answer makes sense — is the angle acute or obtuse?

3. Angles on a Straight Line

Angles on a straight line always add up to 180°.

Example: Two angles on a straight line are 65° and ?°

Missing angle = 180° − 65° = 115°

4. Angles at a Point

Angles around a full point add up to 360°.

Example: Three angles at a point are 100°, 130° and ?°

Missing angle = 360° − 100° − 130° = 130°

5. Angles in Triangles and Quadrilaterals

Angles in a triangle always add up to 180°.

Angles in a quadrilateral always add up to 360°.

Triangle example: Two angles are 70° and 50°.

Third angle = 180° − 70° − 50° = 60°

Quadrilateral example: Three angles are 80°, 110°, 95°.

Fourth angle = 360° − 80° − 110° − 95° = 75°

📐 Worked Examples

Example 1 — Identify the Angle Type

What type of angle is 135°?

135° is between 90° and 180°, so it is an obtuse angle.

Example 2 — Straight Line

An angle of 42° sits on a straight line. Find the other angle.

Other angle = 180° − 42° = 138°

Example 3 — Angles at a Point

Four angles at a point are 90°, 85°, 110°, and ?°.

? = 360° − 90° − 85° − 110° = 75°

Example 4 — Triangle

A triangle has angles 55° and 75°. What is the third angle?

Third angle = 180° − 55° − 75° = 50°

Example 5 — Quadrilateral

A quadrilateral has angles 90°, 90°, 105°. Find the fourth angle.

Fourth angle = 360° − 90° − 90° − 105° = 75°

🔭 Angle Visualizer

Missing Angle Calculator

Type

Angle A (°)

Angle B (°)

Angle C (°)

Angle Type Identifier

Enter angle (°)

Exercise 1 — Identify Angle Types

Enter the type number: 1=Acute, 2=Right, 3=Obtuse, 4=Straight, 5=Reflex, 6=Full

1. What type is 45°?
2. What type is 90°?
3. What type is 120°?
4. What type is 180°?
5. What type is 200°?
6. What type is 360°?
7. What type is 15°?
8. What type is 95°?
9. What type is 270°?
10. What type is 89°?

Exercise 2 — Angles on a Straight Line

All angles sit on a straight line (sum = 180°). Find the missing angle.

1. One angle is 50°. Find the other. °
2. One angle is 110°. Find the other. °
3. One angle is 35°. Find the other. °
4. One angle is 75°. Find the other. °
5. One angle is 90°. Find the other. °
6. Two angles are 60° and 70°. Find the third. °
7. Two angles are 45° and 45°. Find the third. °
8. One angle is 128°. Find the other. °
9. Two angles are 30° and 100°. Find the third. °
10. One angle is 165°. Find the other. °

Exercise 3 — Angles at a Point (360°)

Angles around a full point add up to 360°. Find the missing angle.

1. One angle is 270°. Find the other. °
2. Two angles are 90° and 90°. Find the third. °
3. Two angles are 100° and 120°. Find the third. °
4. Three angles are 80°, 90°, 100°. Find the fourth. °
5. Two angles are 150° and 130°. Find the third. °
6. One angle is 180°. Find the other. °
7. Three angles are 60°, 60°, 120°. Find the fourth. °
8. Two angles are 45° and 45°. Find the third. °
9. Three angles are 70°, 80°, 90°. Find the fourth. °
10. Two angles are 200° and 100°. Find the third. °

Exercise 4 — Angles in Triangles

The three angles of a triangle always add up to 180°. Find the missing angle.

1. A triangle has angles 60° and 60°. Find the third. °
2. Angles are 90° and 45°. Find the third. °
3. Angles are 50° and 70°. Find the third. °
4. Angles are 30° and 120°. Find the third. °
5. Angles are 55° and 65°. Find the third. °
6. Angles are 40° and 100°. Find the third. °
7. Angles are 80° and 80°. Find the third. °
8. Angles are 25° and 135°. Find the third. °
9. Angles are 72° and 63°. Find the third. °
10. Angles are 15° and 90°. Find the third. °

Exercise 5 — Angles in Quadrilaterals

Angles in a quadrilateral add up to 360°. Find the missing angle.

1. Angles are 90°, 90°, 90°. Find the fourth. °
2. Angles are 80°, 100°, 70°. Find the fourth. °
3. Angles are 110°, 85°, 95°. Find the fourth. °
4. Angles are 60°, 60°, 120°. Find the fourth. °
5. Angles are 90°, 90°, 120°. Find the fourth. °
6. Angles are 100°, 100°, 100°. Find the fourth. °
7. Angles are 50°, 130°, 80°. Find the fourth. °
8. Angles are 75°, 85°, 115°. Find the fourth. °
9. Angles are 45°, 135°, 90°. Find the fourth. °
10. Angles are 72°, 108°, 90°. Find the fourth. °

Practice — 20 Questions

Mix of all angle topics. Good luck!

1. What type of angle is 30°? (1=Acute,2=Right,3=Obtuse,4=Straight,5=Reflex,6=Full)
2. Angles on a straight line: one angle is 65°. Find the other. °
3. Triangle angles: 80° and 60°. Find the third. °
4. Angles at a point: two angles are 110° and 140°. Find the third. °
5. What type is 180°? (use number code)
6. Quadrilateral angles: 90°, 90°, 80°. Find the fourth. °
7. Straight line: angles are 40° and ?. Find missing. °
8. What type is 91°? (use number code)
9. Triangle angles: 45° and 90°. Find the third. °
10. Full turn: one angle is 310°. Find the other. °
11. What type is 359°? (use number code)
12. Straight line: one angle is 23°. Find the other. °
13. Triangle: angles are 100° and 35°. Find the third. °
14. Quadrilateral: angles 70°, 80°, 90°. Find the fourth. °
15. Angles at a point: three angles are 90°, 90°, 90°. Find the fourth. °
16. What type is 360°? (use number code)
17. Straight line: two angles are 70° and 50°. Find the third. °
18. Triangle: angles are 33° and 67°. Find the third. °
19. Quadrilateral: angles 110°, 110°, 70°. Find the fourth. °
20. What type is 179°? (use number code)

Challenge — 8 Hard Questions

Multi-step problems — think carefully!

1. An isosceles triangle has two equal angles of 55°. What is the third angle? °
2. A straight line is split into 3 equal angles. What is each angle? °
3. A quadrilateral has three equal angles of 80°. Find the fourth. °
4. One angle at a point is 4 times another. They are the only two angles. Find the smaller angle. °
5. An isosceles triangle has a top angle of 40°. What are the two base angles? (enter one value) °
6. Two angles on a straight line are in the ratio 2:1. What is the larger angle? °
7. A regular hexagon has 6 equal interior angles. Each interior angle = 720° ÷ 6. What is each angle? °
8. In a triangle, angle A = 2×angle B, and angle C = 3×angle B. Find angle B. °