Success TutoringWorksheets

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

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheet7th Grade · Mathematics · Angles

7th 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 30-sided polygon.

Answer: 168°

  1. Angle sum = (30 − 2) × 180° = 5,040°
  2. 5,040° ÷ 30 = 168°
2.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
3.The interior angles of a hexagon are 70°, 163°, 96°, 136°, 132° and x°. Find x.

Answer: 123°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 70 − 163 − 96 − 136 − 132 = 123
4.Each interior angle of a regular polygon is 170°. How many sides does it have?

Answer: 36

  1. Each exterior angle = 180° − 170° = 10°
  2. 360 ÷ 10 = 36 sides
5.The interior angles of a polygon add up to 1,620°. How many sides does it have?

Answer: 11

  1. (n − 2) × 180 = 1,620
  2. n − 2 = 1,620 ÷ 180 = 9, so n = 11
6.Find the size of each interior angle of a regular 24-sided polygon.

Answer: 165°

  1. Angle sum = (24 − 2) × 180° = 3,960°
  2. 3,960° ÷ 24 = 165°
7.Each exterior angle of a regular polygon is 90°. How many sides does it have?

Answer: 4

  1. Exterior angles add to 360°
  2. 360 ÷ 90 = 4 sides
8.The interior angles of a pentagon are 155°, 131°, 70°, 74° and x°. Find x.

Answer: 110°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 155 − 131 − 70 − 74 = 110
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 2,340°. How many sides does it have?

Answer: 15

  1. (n − 2) × 180 = 2,340
  2. n − 2 = 2,340 ÷ 180 = 13, so n = 15
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.