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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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Year 8 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 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 90°. How many sides does it have?

Answer: 4

  1. Exterior angles add to 360°
  2. 360 ÷ 90 = 4 sides
3.The interior angles of a pentagon are 110°, 90°, 83°, 161° and x°. Find x.

Answer: 96°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 110 − 90 − 83 − 161 = 96
4.Each interior angle of a regular polygon is 160°. How many sides does it have?

Answer: 18

  1. Each exterior angle = 180° − 160° = 20°
  2. 360 ÷ 20 = 18 sides
5.The interior angles of a polygon add up to 1,260°. How many sides does it have?

Answer: 9

  1. (n − 2) × 180 = 1,260
  2. n − 2 = 1,260 ÷ 180 = 7, so n = 9
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 30°. How many sides does it have?

Answer: 12

  1. Exterior angles add to 360°
  2. 360 ÷ 30 = 12 sides
8.The interior angles of a pentagon are 117°, 133°, 97°, 74° and x°. Find x.

Answer: 119°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 117 − 133 − 97 − 74 = 119
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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