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7th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 2 — Answers

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

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7th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 2 — 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 pentagon.

Answer: 108°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. 540° ÷ 5 = 108°
2.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
3.The interior angles of a heptagon are 133°, 153°, 157°, 77°, 86°, 159° and x°. Find x.

Answer: 135°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 133 − 153 − 157 − 77 − 86 − 159 = 135
4.Each interior angle of a regular polygon is 108°. How many sides does it have?

Answer: 5

  1. Each exterior angle = 180° − 108° = 72°
  2. 360 ÷ 72 = 5 sides
5.The interior angles of a polygon add up to 3,240°. How many sides does it have?

Answer: 20

  1. (n − 2) × 180 = 3,240
  2. n − 2 = 3,240 ÷ 180 = 18, so n = 20
6.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°
7.Each exterior angle of a regular polygon is 72°. How many sides does it have?

Answer: 5

  1. Exterior angles add to 360°
  2. 360 ÷ 72 = 5 sides
8.The interior angles of a pentagon are 161°, 86°, 132°, 87° and x°. Find x.

Answer: 74°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 161 − 86 − 132 − 87 = 74
9.Each interior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Each exterior angle = 180° − 90° = 90°
  2. 360 ÷ 90 = 4 sides
10.The interior angles of a polygon add up to 1,080°. How many sides does it have?

Answer: 8

  1. (n − 2) × 180 = 1,080
  2. n − 2 = 1,080 ÷ 180 = 6, so n = 8
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