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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 decagon.

Answer: 144°

  1. Angle sum = (10 − 2) × 180° = 1,440°
  2. 1,440° ÷ 10 = 144°
2.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
3.The interior angles of a hexagon are 138°, 157°, 165°, 97°, 101° and x°. Find x.

Answer: 62°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 138 − 157 − 165 − 97 − 101 = 62
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 3,060°. How many sides does it have?

Answer: 19

  1. (n − 2) × 180 = 3,060
  2. n − 2 = 3,060 ÷ 180 = 17, so n = 19
6.Find the size of each interior angle of a regular hexagon.

Answer: 120°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. 720° ÷ 6 = 120°
7.Each exterior angle of a regular polygon is 18°. How many sides does it have?

Answer: 20

  1. Exterior angles add to 360°
  2. 360 ÷ 18 = 20 sides
8.The interior angles of a pentagon are 74°, 116°, 140°, 126° and x°. Find x.

Answer: 84°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 74 − 116 − 140 − 126 = 84
9.Each interior angle of a regular polygon is 168°. How many sides does it have?

Answer: 30

  1. Each exterior angle = 180° − 168° = 12°
  2. 360 ÷ 12 = 30 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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