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Year 7 Angles in Polygons Worksheet — Level 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 7 · Mathematics · Angles

Year 7 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 24-sided polygon.

Answer: 165°

  1. Angle sum = (24 − 2) × 180° = 3,960°
  2. 3,960° ÷ 24 = 165°
2.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
3.The interior angles of a pentagon are 74°, 104°, 105°, 83° and x°. Find x.

Answer: 174°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 74 − 104 − 105 − 83 = 174
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 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
6.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°
7.Each exterior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Exterior angles add to 360°
  2. 360 ÷ 90 = 4 sides
8.The interior angles of a hexagon are 107°, 112°, 165°, 145°, 72° and x°. Find x.

Answer: 119°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 107 − 112 − 165 − 145 − 72 = 119
9.Each interior angle of a regular polygon is 162°. How many sides does it have?

Answer: 20

  1. Each exterior angle = 180° − 162° = 18°
  2. 360 ÷ 18 = 20 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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