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Year 9 Angles in Polygons Worksheet — Level 3 — Practice Set 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Angles

Year 9 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 40°. How many sides does it have?

Answer: 9

  1. Exterior angles add to 360°
  2. 360 ÷ 40 = 9 sides
3.The interior angles of a hexagon are 149°, 98°, 106°, 131°, 82° and x°. Find x.

Answer: 154°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 149 − 98 − 106 − 131 − 82 = 154
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 540°. How many sides does it have?

Answer: 5

  1. (n − 2) × 180 = 540
  2. n − 2 = 540 ÷ 180 = 3, so n = 5
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.Each exterior angle of a regular polygon is 10°. How many sides does it have?

Answer: 36

  1. Exterior angles add to 360°
  2. 360 ÷ 10 = 36 sides
8.The interior angles of a pentagon are 154°, 112°, 73°, 76° and x°. Find x.

Answer: 125°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 154 − 112 − 73 − 76 = 125
9.Each interior angle of a regular polygon is 140°. How many sides does it have?

Answer: 9

  1. Each exterior angle = 180° − 140° = 40°
  2. 360 ÷ 40 = 9 sides
10.The interior angles of a polygon add up to 1,080°. How many sides does it have?

Answer: 8

  1. (n − 2) × 180 = 1,080
  2. n − 2 = 1,080 ÷ 180 = 6, so n = 8
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