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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 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 36°. How many sides does it have?

Answer: 10

  1. Exterior angles add to 360°
  2. 360 ÷ 36 = 10 sides
3.The interior angles of a heptagon are 75°, 86°, 152°, 129°, 154°, 150° and x°. Find x.

Answer: 154°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 75 − 86 − 152 − 129 − 154 − 150 = 154
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 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
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 pentagon are 116°, 82°, 140°, 87° and x°. Find x.

Answer: 115°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 116 − 82 − 140 − 87 = 115
9.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
10.The interior angles of a polygon add up to 2,160°. How many sides does it have?

Answer: 14

  1. (n − 2) × 180 = 2,160
  2. n − 2 = 2,160 ÷ 180 = 12, so n = 14
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