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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 15-sided polygon.

Answer: 156°

  1. Angle sum = (15 − 2) × 180° = 2,340°
  2. 2,340° ÷ 15 = 156°
2.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
3.The interior angles of a hexagon are 137°, 134°, 78°, 116°, 142° and x°. Find x.

Answer: 113°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 137 − 134 − 78 − 116 − 142 = 113
4.Each interior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Each exterior angle = 180° − 90° = 90°
  2. 360 ÷ 90 = 4 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 18-sided polygon.

Answer: 160°

  1. Angle sum = (18 − 2) × 180° = 2,880°
  2. 2,880° ÷ 18 = 160°
7.Each exterior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Exterior angles add to 360°
  2. 360 ÷ 90 = 4 sides
8.The interior angles of a pentagon are 137°, 91°, 131°, 106° and x°. Find x.

Answer: 75°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 137 − 91 − 131 − 106 = 75
9.Each interior angle of a regular polygon is 135°. How many sides does it have?

Answer: 8

  1. Each exterior angle = 180° − 135° = 45°
  2. 360 ÷ 45 = 8 sides
10.The interior angles of a polygon add up to 2,520°. How many sides does it have?

Answer: 16

  1. (n − 2) × 180 = 2,520
  2. n − 2 = 2,520 ÷ 180 = 14, so n = 16
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