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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 24°. How many sides does it have?

Answer: 15

  1. Exterior angles add to 360°
  2. 360 ÷ 24 = 15 sides
3.The interior angles of a heptagon are 131°, 84°, 125°, 144°, 138°, 124° and x°. Find x.

Answer: 154°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 131 − 84 − 125 − 144 − 138 − 124 = 154
4.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
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 dodecagon.

Answer: 150°

  1. Angle sum = (12 − 2) × 180° = 1,800°
  2. 1,800° ÷ 12 = 150°
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 quadrilateral are 128°, 98°, 70° and x°. Find x.

Answer: 64°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 128 − 98 − 70 = 64
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 2,340°. How many sides does it have?

Answer: 15

  1. (n − 2) × 180 = 2,340
  2. n − 2 = 2,340 ÷ 180 = 13, so n = 15
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