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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 quadrilateral.

Answer: 90°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. 360° ÷ 4 = 90°
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 133°, 139°, 142°, 113°, 169°, 110° and x°. Find x.

Answer: 94°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 133 − 139 − 142 − 113 − 169 − 110 = 94
4.Each interior angle of a regular polygon is 170°. How many sides does it have?

Answer: 36

  1. Each exterior angle = 180° − 170° = 10°
  2. 360 ÷ 10 = 36 sides
5.The interior angles of a polygon add up to 2,880°. How many sides does it have?

Answer: 18

  1. (n − 2) × 180 = 2,880
  2. n − 2 = 2,880 ÷ 180 = 16, so n = 18
6.Find the size of each interior angle of a regular dodecagon.

Answer: 150°

  1. Angle sum = (12 − 2) × 180° = 1,800°
  2. 1,800° ÷ 12 = 150°
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 pentagon are 78°, 116°, 152°, 98° and x°. Find x.

Answer: 96°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 78 − 116 − 152 − 98 = 96
9.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
10.The interior angles of a polygon add up to 1,080°. How many sides does it have?

Answer: 8

  1. (n − 2) × 180 = 1,080
  2. n − 2 = 1,080 ÷ 180 = 6, so n = 8
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