Why is the sum of the interior angles of a pentagon 540°?

It splits into 3 triangles from one corner, and 3 × 180° = 540°

It splits into 5 triangles, and 5 × 108° = 540°

It has 5 angles of 108°, and every pentagon is regular

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Math 9 · Unit 5: Angles · Cambridge Lower Secondary Maths Stage 9

5.2 Interior angles of polygons

22 questions · e.g. Could the interior angles of a polygon add up to 800°?

Practice

Questions

1. Work out the sum of the interior angles of a polygon with 4 sides.
- 360°
- 180°
- 540°
- 720°
Check
2. What is the sum of the interior angles of an octagon?
- 900°
- 1440°
- 1080°
- 720°
Check
3. What is the sum of the interior angles of a 12-sided polygon?
- 1080°
- 1620°
- 1800°
- 2160°
Check
4. Why is the sum of the interior angles of a pentagon 540°?
- 5 × 180° = 540°
- It splits into 5 triangles, and 5 × 108° = 540°
- It has 5 angles of 108°, and every pentagon is regular
- It splits into 3 triangles from one corner, and 3 × 180° = 540°
Check
5. Four interior angles of a pentagon are 120°. What is the fifth angle?
- 120°
- 60°
- 108°
- 90°
Check
6. Four of the interior angles of a pentagon are 108°. Is it definitely a regular polygon?
- Yes
- No
Check
7. What is the sum of the interior angles of a nonagon (9 sides)?
- 1620°
- 1080°
- 1260°
- 1440°
Check
8. What is each interior angle of a regular nonagon?
- 120°
- 135°
- 160°
- 140°
Check
9. The interior angles of a polygon add up to 900°. How many sides does it have?
- 6
- 5
- 7
- 9
Check
10. Marcus says: "I have drawn a polygon. The sum of the interior angles is 800°." Is this possible?
- Yes
- No
Check
11. Look at this diagram. Sofia says: "There are 6 right angles in this hexagon. So the sum of the interior angles is 6 × 90° = 540°." Is Sofia correct?
- Yes
- No
Check
12. The angles of a pentagon are x°, x°, x°, x° and (x + 10)°. Work out the value of x.
- 108
- 110
- 106
- 116
Check
13. Work out the sum of the angles of this shape.
- 1260°
- 720°
- 900°
- 1080°
Check
14. Work out the value of x.
- 40
- 60
- 130
- 50
Check
15. True or false: the sum of the interior angles of a polygon could be 1800°, but could not be 2000°.
- True
- False
Check
16. Two regular octagons and a square meet at a point as shown. Do they fit together with no gaps?
- Yes
- No
Check
17. Which mixture of regular hexagons and equilateral triangles fits round a point?
- 1 hexagon and 4 triangles
- 2 hexagons and 1 triangle
- 3 hexagons and 1 triangle
- 1 hexagon and 3 triangles
Check
18. Work out the sum of the interior angles of a decagon (10 sides).
- 1260°
- 1800°
- 1440°
- 144°
Check
19. This diagram shows two regular pentagons and part of another regular shape arranged round a point. Is the third shape a decagon?
- Yes
- No
Check
20. A star has 4 lines of symmetry and rotational symmetry of order 4. Outside the star, the angle between two points is 120°. Work out the angle of each point.
- 45°
- 120°
- 30°
- 60°
Check