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Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — Answers

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Angles

Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — 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 12°. How many sides does it have?

Answer: 30

  1. Exterior angles add to 360°
  2. 360 ÷ 12 = 30 sides
3.The interior angles of a hexagon are 89°, 80°, 159°, 120°, 130° and x°. Find x.

Answer: 142°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 89 − 80 − 159 − 120 − 130 = 142
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 2,520°. How many sides does it have?

Answer: 16

  1. (n − 2) × 180 = 2,520
  2. n − 2 = 2,520 ÷ 180 = 14, so n = 16
6.Find the size of each interior angle of a regular octagon.

Answer: 135°

  1. Angle sum = (8 − 2) × 180° = 1,080°
  2. 1,080° ÷ 8 = 135°
7.Each exterior angle of a regular polygon is 36°. How many sides does it have?

Answer: 10

  1. Exterior angles add to 360°
  2. 360 ÷ 36 = 10 sides
8.The interior angles of a quadrilateral are 86°, 73°, 81° and x°. Find x.

Answer: 120°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 86 − 73 − 81 = 120
9.Each interior angle of a regular polygon is 170°. How many sides does it have?

Answer: 36

  1. Each exterior angle = 180° − 170° = 10°
  2. 360 ÷ 10 = 36 sides
10.The interior angles of a polygon add up to 3,240°. How many sides does it have?

Answer: 20

  1. (n − 2) × 180 = 3,240
  2. n − 2 = 3,240 ÷ 180 = 18, so n = 20
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