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8th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 4 — Answers

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8th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 4 — 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 nonagon.

Answer: 140°

  1. Angle sum = (9 − 2) × 180° = 1,260°
  2. 1,260° ÷ 9 = 140°
2.Each exterior angle of a regular polygon is 15°. How many sides does it have?

Answer: 24

  1. Exterior angles add to 360°
  2. 360 ÷ 15 = 24 sides
3.The interior angles of a hexagon are 102°, 163°, 80°, 149°, 104° and x°. Find x.

Answer: 122°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 102 − 163 − 80 − 149 − 104 = 122
4.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
5.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
6.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°
7.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
8.The interior angles of a pentagon are 84°, 121°, 82°, 170° and x°. Find x.

Answer: 83°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 84 − 121 − 82 − 170 = 83
9.Each interior angle of a regular polygon is 144°. How many sides does it have?

Answer: 10

  1. Each exterior angle = 180° − 144° = 36°
  2. 360 ÷ 36 = 10 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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