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

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Year 8 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 20-sided polygon.

Answer: 162°

  1. Angle sum = (20 − 2) × 180° = 3,240°
  2. 3,240° ÷ 20 = 162°
2.Each exterior angle of a regular polygon is 12°. How many sides does it have?

Answer: 30

  1. Exterior angles add to 360°
  2. 360 ÷ 12 = 30 sides
3.The interior angles of a heptagon are 156°, 123°, 153°, 169°, 95°, 136° and x°. Find x.

Answer: 68°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 156 − 123 − 153 − 169 − 95 − 136 = 68
4.Each interior angle of a regular polygon is 160°. How many sides does it have?

Answer: 18

  1. Each exterior angle = 180° − 160° = 20°
  2. 360 ÷ 20 = 18 sides
5.The interior angles of a polygon add up to 1,980°. How many sides does it have?

Answer: 13

  1. (n − 2) × 180 = 1,980
  2. n − 2 = 1,980 ÷ 180 = 11, so n = 13
6.Find the size of each interior angle of a regular quadrilateral.

Answer: 90°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. 360° ÷ 4 = 90°
7.Each exterior angle of a regular polygon is 24°. How many sides does it have?

Answer: 15

  1. Exterior angles add to 360°
  2. 360 ÷ 24 = 15 sides
8.The interior angles of a heptagon are 168°, 108°, 107°, 96°, 137°, 127° and x°. Find x.

Answer: 157°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 168 − 108 − 107 − 96 − 137 − 127 = 157
9.Each interior angle of a regular polygon is 135°. How many sides does it have?

Answer: 8

  1. Each exterior angle = 180° − 135° = 45°
  2. 360 ÷ 45 = 8 sides
10.The interior angles of a polygon add up to 900°. How many sides does it have?

Answer: 7

  1. (n − 2) × 180 = 900
  2. n − 2 = 900 ÷ 180 = 5, so n = 7
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