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7th Grade Angles in Polygons Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 7th Grade angles worksheet.

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Success TutoringWorksheetsAnswer sheet7th Grade · Mathematics · Angles

7th Grade 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 triangle.

Answer: 60°

  1. Angle sum = (3 − 2) × 180° = 180°
  2. 180° ÷ 3 = 60°
2.Each exterior angle of a regular polygon is 24°. How many sides does it have?

Answer: 15

  1. Exterior angles add to 360°
  2. 360 ÷ 24 = 15 sides
3.The interior angles of a heptagon are 165°, 71°, 138°, 165°, 99°, 110° and x°. Find x.

Answer: 152°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 165 − 71 − 138 − 165 − 99 − 110 = 152
4.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
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 hexagon.

Answer: 120°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. 720° ÷ 6 = 120°
7.Each exterior angle of a regular polygon is 60°. How many sides does it have?

Answer: 6

  1. Exterior angles add to 360°
  2. 360 ÷ 60 = 6 sides
8.The interior angles of a hexagon are 146°, 131°, 142°, 83°, 152° and x°. Find x.

Answer: 66°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 146 − 131 − 142 − 83 − 152 = 66
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 2,520°. How many sides does it have?

Answer: 16

  1. (n − 2) × 180 = 2,520
  2. n − 2 = 2,520 ÷ 180 = 14, so n = 16
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