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Year 7 Angles in Polygons Worksheet — Level 2 — Practice Set 4 — Answers

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Year 7 Angles in Polygons Worksheet — Level 2 — Practice Set 4 — Answers

Interior angle sum = (n − 2) × 180°. The exterior angles of any convex polygon add to 360°.

1.Find the sum of the interior angles of a dodecagon.

Answer: 1,800°

  1. Angle sum = (n − 2) × 180°
  2. (12 − 2) × 180° = 1,800°
2.Find the size of each interior angle of a regular 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
3.Find the size of each exterior angle of a regular quadrilateral.

Answer: 90°

  1. Exterior angles add to 360°
  2. 360° ÷ 4 = 90°
4.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
5.Find the sum of the interior angles of a 11-sided polygon.

Answer: 1,620°

  1. Angle sum = (n − 2) × 180°
  2. (11 − 2) × 180° = 1,620°
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.Find the size of each exterior angle of a regular 36-sided polygon.

Answer: 10°

  1. Exterior angles add to 360°
  2. 360° ÷ 36 = 10°
8.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
9.Find the sum of the interior angles of a 20-sided polygon.

Answer: 3,240°

  1. Angle sum = (n − 2) × 180°
  2. (20 − 2) × 180° = 3,240°
10.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°
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