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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 3 — Answers

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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 3 — Answers

Interior angle sum = (n − 2) × 180°. The exterior angles of any convex polygon add to 360°.

1.Find the size of each interior angle of a regular decagon.

Answer: 144°

  1. Angle sum = (10 − 2) × 180° = 1,440°
  2. 1,440° ÷ 10 = 144°
2.Each exterior angle of a regular polygon is 60°. How many sides does it have?

Answer: 6

  1. Exterior angles add to 360°
  2. 360 ÷ 60 = 6 sides
3.The interior angles of a pentagon are 107°, 80°, 162°, 92° and x°. Find x.

Answer: 99°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 107 − 80 − 162 − 92 = 99
4.Each interior angle of a regular polygon is 162°. How many sides does it have?

Answer: 20

  1. Each exterior angle = 180° − 162° = 18°
  2. 360 ÷ 18 = 20 sides
5.The interior angles of a polygon add up to 1,440°. How many sides does it have?

Answer: 10

  1. (n − 2) × 180 = 1,440
  2. n − 2 = 1,440 ÷ 180 = 8, so n = 10
6.Find the size of each interior angle of a regular 20-sided polygon.

Answer: 162°

  1. Angle sum = (20 − 2) × 180° = 3,240°
  2. 3,240° ÷ 20 = 162°
7.Each exterior angle of a regular polygon is 45°. How many sides does it have?

Answer: 8

  1. Exterior angles add to 360°
  2. 360 ÷ 45 = 8 sides
8.The interior angles of a quadrilateral are 124°, 93°, 70° and x°. Find x.

Answer: 73°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 124 − 93 − 70 = 73
9.Each interior angle of a regular polygon is 144°. How many sides does it have?

Answer: 10

  1. Each exterior angle = 180° − 144° = 36°
  2. 360 ÷ 36 = 10 sides
10.The interior angles of a polygon add up to 1,260°. How many sides does it have?

Answer: 9

  1. (n − 2) × 180 = 1,260
  2. n − 2 = 1,260 ÷ 180 = 7, so n = 9
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