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Year 9 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Angles

Year 9 Angles in Polygons Worksheet — Level 3 — Practice Set 4 — 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 octagon.

Answer: 135°

  1. Angle sum = (8 − 2) × 180° = 1,080°
  2. 1,080° ÷ 8 = 135°
2.Each exterior angle of a regular polygon is 72°. How many sides does it have?

Answer: 5

  1. Exterior angles add to 360°
  2. 360 ÷ 72 = 5 sides
3.The interior angles of a hexagon are 133°, 151°, 79°, 133°, 104° and x°. Find x.

Answer: 120°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 133 − 151 − 79 − 133 − 104 = 120
4.Each interior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Each exterior angle = 180° − 90° = 90°
  2. 360 ÷ 90 = 4 sides
5.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
6.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°
7.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
8.The interior angles of a quadrilateral are 73°, 84°, 106° and x°. Find x.

Answer: 97°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 73 − 84 − 106 = 97
9.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
10.The interior angles of a polygon add up to 2,700°. How many sides does it have?

Answer: 17

  1. (n − 2) × 180 = 2,700
  2. n − 2 = 2,700 ÷ 180 = 15, so n = 17
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