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Year 9 Angles in Polygons Worksheet — Level 3 — Practice Set 2 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Angles

Year 9 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 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 45°. How many sides does it have?

Answer: 8

  1. Exterior angles add to 360°
  2. 360 ÷ 45 = 8 sides
3.The interior angles of a heptagon are 159°, 74°, 145°, 150°, 147°, 96° and x°. Find x.

Answer: 129°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 159 − 74 − 145 − 150 − 147 − 96 = 129
4.Each interior angle of a regular polygon is 108°. How many sides does it have?

Answer: 5

  1. Each exterior angle = 180° − 108° = 72°
  2. 360 ÷ 72 = 5 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 15-sided polygon.

Answer: 156°

  1. Angle sum = (15 − 2) × 180° = 2,340°
  2. 2,340° ÷ 15 = 156°
7.Each exterior angle of a regular polygon is 10°. How many sides does it have?

Answer: 36

  1. Exterior angles add to 360°
  2. 360 ÷ 10 = 36 sides
8.The interior angles of a pentagon are 155°, 118°, 80°, 108° and x°. Find x.

Answer: 79°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 155 − 118 − 80 − 108 = 79
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 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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