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Year 9 Angles in Polygons Worksheet — Level 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Angles

Year 9 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 pentagon.

Answer: 108°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. 540° ÷ 5 = 108°
2.Each exterior angle of a regular polygon is 15°. How many sides does it have?

Answer: 24

  1. Exterior angles add to 360°
  2. 360 ÷ 15 = 24 sides
3.The interior angles of a heptagon are 87°, 124°, 166°, 91°, 112°, 162° and x°. Find x.

Answer: 158°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 87 − 124 − 166 − 91 − 112 − 162 = 158
4.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
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 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 40°. How many sides does it have?

Answer: 9

  1. Exterior angles add to 360°
  2. 360 ÷ 40 = 9 sides
8.The interior angles of a pentagon are 117°, 154°, 70°, 79° and x°. Find x.

Answer: 120°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 117 − 154 − 70 − 79 = 120
9.Each interior angle of a regular polygon is 165°. How many sides does it have?

Answer: 24

  1. Each exterior angle = 180° − 165° = 15°
  2. 360 ÷ 15 = 24 sides
10.The interior angles of a polygon add up to 2,880°. How many sides does it have?

Answer: 18

  1. (n − 2) × 180 = 2,880
  2. n − 2 = 2,880 ÷ 180 = 16, so n = 18
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