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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 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
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 heptagon are 138°, 159°, 74°, 161°, 147°, 114° and x°. Find x.

Answer: 107°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 138 − 159 − 74 − 161 − 147 − 114 = 107
4.Each interior angle of a regular polygon is 108°. How many sides does it have?

Answer: 5

  1. Each exterior angle = 180° − 108° = 72°
  2. 360 ÷ 72 = 5 sides
5.The interior angles of a polygon add up to 2,340°. How many sides does it have?

Answer: 15

  1. (n − 2) × 180 = 2,340
  2. n − 2 = 2,340 ÷ 180 = 13, so n = 15
6.Find the size of each interior angle of a regular nonagon.

Answer: 140°

  1. Angle sum = (9 − 2) × 180° = 1,260°
  2. 1,260° ÷ 9 = 140°
7.Each exterior angle of a regular polygon is 10°. How many sides does it have?

Answer: 36

  1. Exterior angles add to 360°
  2. 360 ÷ 10 = 36 sides
8.The interior angles of a hexagon are 140°, 105°, 94°, 124°, 144° and x°. Find x.

Answer: 113°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 140 − 105 − 94 − 124 − 144 = 113
9.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
10.The interior angles of a polygon add up to 1,800°. How many sides does it have?

Answer: 12

  1. (n − 2) × 180 = 1,800
  2. n − 2 = 1,800 ÷ 180 = 10, so n = 12
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