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Year 7 Angles in Polygons Worksheet — Level 1 — Practice Set 4 — Answers

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Year 7 Angles in Polygons Worksheet — Level 1 — 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 hexagon.

Answer: 720°

  1. Angle sum = (n − 2) × 180°
  2. (6 − 2) × 180° = 720°
2.Find the size of each interior angle of a regular 20-sided polygon.

Answer: 162°

  1. Angle sum = (20 − 2) × 180° = 3,240°
  2. 3,240° ÷ 20 = 162°
3.Find the sum of the interior angles of a pentagon.

Answer: 540°

  1. Angle sum = (n − 2) × 180°
  2. (5 − 2) × 180° = 540°
4.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°
5.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°
6.Find the size of each interior angle of a regular 24-sided polygon.

Answer: 165°

  1. Angle sum = (24 − 2) × 180° = 3,960°
  2. 3,960° ÷ 24 = 165°
7.Find the sum of the interior angles of a quadrilateral.

Answer: 360°

  1. Angle sum = (n − 2) × 180°
  2. (4 − 2) × 180° = 360°
8.Find the size of each interior angle of a regular quadrilateral.

Answer: 90°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. 360° ÷ 4 = 90°
9.Find the sum of the interior angles of a 15-sided polygon.

Answer: 2,340°

  1. Angle sum = (n − 2) × 180°
  2. (15 − 2) × 180° = 2,340°
10.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°
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