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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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Year 7 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — 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 decagon.

Answer: 144°

  1. Angle sum = (10 − 2) × 180° = 1,440°
  2. 1,440° ÷ 10 = 144°
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 pentagon are 107°, 109°, 115°, 106° and x°. Find x.

Answer: 103°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 107 − 109 − 115 − 106 = 103
4.Each interior angle of a regular polygon is 144°. How many sides does it have?

Answer: 10

  1. Each exterior angle = 180° − 144° = 36°
  2. 360 ÷ 36 = 10 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 quadrilateral.

Answer: 90°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. 360° ÷ 4 = 90°
7.Each exterior angle of a regular polygon is 45°. How many sides does it have?

Answer: 8

  1. Exterior angles add to 360°
  2. 360 ÷ 45 = 8 sides
8.The interior angles of a heptagon are 142°, 124°, 125°, 153°, 117°, 97° and x°. Find x.

Answer: 142°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 142 − 124 − 125 − 153 − 117 − 97 = 142
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 720°. How many sides does it have?

Answer: 6

  1. (n − 2) × 180 = 720
  2. n − 2 = 720 ÷ 180 = 4, so n = 6
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