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Year 7 Angles in Polygons Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 7 angles worksheet.

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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 pentagon.

Answer: 108°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. 540° ÷ 5 = 108°
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 hexagon are 112°, 95°, 76°, 130°, 147° and x°. Find x.

Answer: 160°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 112 − 95 − 76 − 130 − 147 = 160
4.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
5.The interior angles of a polygon add up to 1,440°. How many sides does it have?

Answer: 10

  1. (n − 2) × 180 = 1,440
  2. n − 2 = 1,440 ÷ 180 = 8, so n = 10
6.Find the size of each interior angle of a regular 18-sided polygon.

Answer: 160°

  1. Angle sum = (18 − 2) × 180° = 2,880°
  2. 2,880° ÷ 18 = 160°
7.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
8.The interior angles of a heptagon are 114°, 129°, 145°, 115°, 132°, 132° and x°. Find x.

Answer: 133°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 114 − 129 − 145 − 115 − 132 − 132 = 133
9.Each interior angle of a regular polygon is 160°. How many sides does it have?

Answer: 18

  1. Each exterior angle = 180° − 160° = 20°
  2. 360 ÷ 20 = 18 sides
10.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
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