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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — Answers

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Year 8 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 18-sided polygon.

Answer: 160°

  1. Angle sum = (18 − 2) × 180° = 2,880°
  2. 2,880° ÷ 18 = 160°
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 pentagon are 97°, 84°, 151°, 136° and x°. Find x.

Answer: 72°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 97 − 84 − 151 − 136 = 72
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 2,700°. How many sides does it have?

Answer: 17

  1. (n − 2) × 180 = 2,700
  2. n − 2 = 2,700 ÷ 180 = 15, so n = 17
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 60°. How many sides does it have?

Answer: 6

  1. Exterior angles add to 360°
  2. 360 ÷ 60 = 6 sides
8.The interior angles of a pentagon are 122°, 72°, 115°, 170° and x°. Find x.

Answer: 61°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 122 − 72 − 115 − 170 = 61
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 2,340°. How many sides does it have?

Answer: 15

  1. (n − 2) × 180 = 2,340
  2. n − 2 = 2,340 ÷ 180 = 13, so n = 15
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