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

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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 3 — 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 nonagon.

Answer: 140°

  1. Angle sum = (9 − 2) × 180° = 1,260°
  2. 1,260° ÷ 9 = 140°
2.Each exterior angle of a regular polygon is 15°. How many sides does it have?

Answer: 24

  1. Exterior angles add to 360°
  2. 360 ÷ 15 = 24 sides
3.The interior angles of a pentagon are 101°, 129°, 70°, 141° and x°. Find x.

Answer: 99°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 101 − 129 − 70 − 141 = 99
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 3,060°. How many sides does it have?

Answer: 19

  1. (n − 2) × 180 = 3,060
  2. n − 2 = 3,060 ÷ 180 = 17, so n = 19
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 heptagon are 79°, 142°, 92°, 165°, 142°, 152° and x°. Find x.

Answer: 128°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 79 − 142 − 92 − 165 − 142 − 152 = 128
9.Each interior angle of a regular polygon is 120°. How many sides does it have?

Answer: 6

  1. Each exterior angle = 180° − 120° = 60°
  2. 360 ÷ 60 = 6 sides
10.The interior angles of a polygon add up to 900°. How many sides does it have?

Answer: 7

  1. (n − 2) × 180 = 900
  2. n − 2 = 900 ÷ 180 = 5, so n = 7
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