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8th Grade Angles in Polygons Worksheet — Level 2 — Practice Set 4 — Answers

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8th Grade Angles in Polygons Worksheet — Level 2 — Practice Set 4 — Answers

Interior angle sum = (n − 2) × 180°. The exterior angles of any convex polygon add to 360°.

1.Find the sum of the interior angles of a quadrilateral.

Answer: 360°

  1. Angle sum = (n − 2) × 180°
  2. (4 − 2) × 180° = 360°
2.Find the size of each interior angle of a regular 36-sided polygon.

Answer: 170°

  1. Angle sum = (36 − 2) × 180° = 6,120°
  2. 6,120° ÷ 36 = 170°
3.Find the size of each exterior angle of a regular decagon.

Answer: 36°

  1. Exterior angles add to 360°
  2. 360° ÷ 10 = 36°
4.Each exterior angle of a regular polygon is 10°. How many sides does it have?

Answer: 36

  1. Exterior angles add to 360°
  2. 360 ÷ 10 = 36 sides
5.Find the sum of the interior angles of an octagon.

Answer: 1,080°

  1. Angle sum = (n − 2) × 180°
  2. (8 − 2) × 180° = 1,080°
6.Find the size of each interior angle of a regular 15-sided polygon.

Answer: 156°

  1. Angle sum = (15 − 2) × 180° = 2,340°
  2. 2,340° ÷ 15 = 156°
7.Find the size of each exterior angle of a regular 36-sided polygon.

Answer: 10°

  1. Exterior angles add to 360°
  2. 360° ÷ 36 = 10°
8.Each exterior angle of a regular polygon is 30°. How many sides does it have?

Answer: 12

  1. Exterior angles add to 360°
  2. 360 ÷ 30 = 12 sides
9.Find the sum of the interior angles of a decagon.

Answer: 1,440°

  1. Angle sum = (n − 2) × 180°
  2. (10 − 2) × 180° = 1,440°
10.Find the size of each interior angle of a regular 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
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