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8th Grade Angles in Polygons Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 8th Grade angles worksheet.

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Success TutoringWorksheetsAnswer sheet8th Grade · Mathematics · Angles

8th 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 18-sided polygon.

Answer: 160°

  1. Angle sum = (18 − 2) × 180° = 2,880°
  2. 2,880° ÷ 18 = 160°
2.Each exterior angle of a regular polygon is 20°. How many sides does it have?

Answer: 18

  1. Exterior angles add to 360°
  2. 360 ÷ 20 = 18 sides
3.The interior angles of a hexagon are 157°, 85°, 99°, 147°, 102° and x°. Find x.

Answer: 130°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 157 − 85 − 99 − 147 − 102 = 130
4.Each interior angle of a regular polygon is 120°. How many sides does it have?

Answer: 6

  1. Each exterior angle = 180° − 120° = 60°
  2. 360 ÷ 60 = 6 sides
5.The interior angles of a polygon add up to 2,880°. How many sides does it have?

Answer: 18

  1. (n − 2) × 180 = 2,880
  2. n − 2 = 2,880 ÷ 180 = 16, so n = 18
6.Find the size of each interior angle of a regular 20-sided polygon.

Answer: 162°

  1. Angle sum = (20 − 2) × 180° = 3,240°
  2. 3,240° ÷ 20 = 162°
7.Each exterior angle of a regular polygon is 36°. How many sides does it have?

Answer: 10

  1. Exterior angles add to 360°
  2. 360 ÷ 36 = 10 sides
8.The interior angles of a quadrilateral are 101°, 102°, 96° and x°. Find x.

Answer: 61°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 101 − 102 − 96 = 61
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 2,160°. How many sides does it have?

Answer: 14

  1. (n − 2) × 180 = 2,160
  2. n − 2 = 2,160 ÷ 180 = 12, so n = 14
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