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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — 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 18°. How many sides does it have?

Answer: 20

  1. Exterior angles add to 360°
  2. 360 ÷ 18 = 20 sides
3.The interior angles of a hexagon are 73°, 161°, 137°, 112°, 159° and x°. Find x.

Answer: 78°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 73 − 161 − 137 − 112 − 159 = 78
4.Each interior angle of a regular polygon is 156°. How many sides does it have?

Answer: 15

  1. Each exterior angle = 180° − 156° = 24°
  2. 360 ÷ 24 = 15 sides
5.The interior angles of a polygon add up to 3,060°. How many sides does it have?

Answer: 19

  1. (n − 2) × 180 = 3,060
  2. n − 2 = 3,060 ÷ 180 = 17, so n = 19
6.Find the size of each interior angle of a regular 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
7.Each exterior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Exterior angles add to 360°
  2. 360 ÷ 90 = 4 sides
8.The interior angles of a hexagon are 161°, 82°, 120°, 99°, 149° and x°. Find x.

Answer: 109°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 161 − 82 − 120 − 99 − 149 = 109
9.Each interior angle of a regular polygon is 168°. How many sides does it have?

Answer: 30

  1. Each exterior angle = 180° − 168° = 12°
  2. 360 ÷ 12 = 30 sides
10.The interior angles of a polygon add up to 1,080°. How many sides does it have?

Answer: 8

  1. (n − 2) × 180 = 1,080
  2. n − 2 = 1,080 ÷ 180 = 6, so n = 8
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