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Year 8 Angles in Polygons Worksheet — Level 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Angles

Year 8 Angles in Polygons Worksheet — Level 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 dodecagon.

Answer: 150°

  1. Angle sum = (12 − 2) × 180° = 1,800°
  2. 1,800° ÷ 12 = 150°
2.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
3.The interior angles of a hexagon are 101°, 116°, 155°, 78°, 125° and x°. Find x.

Answer: 145°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 101 − 116 − 155 − 78 − 125 = 145
4.Each interior angle of a regular polygon is 150°. How many sides does it have?

Answer: 12

  1. Each exterior angle = 180° − 150° = 30°
  2. 360 ÷ 30 = 12 sides
5.The interior angles of a polygon add up to 2,160°. How many sides does it have?

Answer: 14

  1. (n − 2) × 180 = 2,160
  2. n − 2 = 2,160 ÷ 180 = 12, so n = 14
6.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°
7.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
8.The interior angles of a heptagon are 110°, 170°, 138°, 111°, 150°, 131° and x°. Find x.

Answer: 90°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 110 − 170 − 138 − 111 − 150 − 131 = 90
9.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
10.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
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