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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — Answers

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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — 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 24-sided polygon.

Answer: 165°

  1. Angle sum = (24 − 2) × 180° = 3,960°
  2. 3,960° ÷ 24 = 165°
2.Each exterior angle of a regular polygon is 20°. How many sides does it have?

Answer: 18

  1. Exterior angles add to 360°
  2. 360 ÷ 20 = 18 sides
3.The interior angles of a heptagon are 154°, 151°, 146°, 119°, 109°, 82° and x°. Find x.

Answer: 139°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 154 − 151 − 146 − 119 − 109 − 82 = 139
4.Each interior angle of a regular polygon is 150°. How many sides does it have?

Answer: 12

  1. Each exterior angle = 180° − 150° = 30°
  2. 360 ÷ 30 = 12 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 hexagon.

Answer: 120°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. 720° ÷ 6 = 120°
7.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
8.The interior angles of a hexagon are 120°, 167°, 146°, 81°, 75° and x°. Find x.

Answer: 131°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 120 − 167 − 146 − 81 − 75 = 131
9.Each interior angle of a regular polygon is 120°. How many sides does it have?

Answer: 6

  1. Each exterior angle = 180° − 120° = 60°
  2. 360 ÷ 60 = 6 sides
10.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
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