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

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

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8th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 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 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 36°. How many sides does it have?

Answer: 10

  1. Exterior angles add to 360°
  2. 360 ÷ 36 = 10 sides
3.The interior angles of a quadrilateral are 106°, 111°, 75° and x°. Find x.

Answer: 68°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 106 − 111 − 75 = 68
4.Each interior angle of a regular polygon is 140°. How many sides does it have?

Answer: 9

  1. Each exterior angle = 180° − 140° = 40°
  2. 360 ÷ 40 = 9 sides
5.The interior angles of a polygon add up to 1,800°. How many sides does it have?

Answer: 12

  1. (n − 2) × 180 = 1,800
  2. n − 2 = 1,800 ÷ 180 = 10, so n = 12
6.Find the size of each interior angle of a regular dodecagon.

Answer: 150°

  1. Angle sum = (12 − 2) × 180° = 1,800°
  2. 1,800° ÷ 12 = 150°
7.Each exterior angle of a regular polygon is 12°. How many sides does it have?

Answer: 30

  1. Exterior angles add to 360°
  2. 360 ÷ 12 = 30 sides
8.The interior angles of a quadrilateral are 101°, 91°, 103° and x°. Find x.

Answer: 65°

  1. Angle sum = (4 − 2) × 180° = 360°
  2. x = 360 − 101 − 91 − 103 = 65
9.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
10.The interior angles of a polygon add up to 720°. How many sides does it have?

Answer: 6

  1. (n − 2) × 180 = 720
  2. n − 2 = 720 ÷ 180 = 4, so n = 6
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