Success TutoringWorksheets

7th Grade Angles in Polygons Worksheet — Level 3 — Practice Set 4 — 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 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 18°. How many sides does it have?

Answer: 20

  1. Exterior angles add to 360°
  2. 360 ÷ 18 = 20 sides
3.The interior angles of a pentagon are 115°, 107°, 77°, 120° and x°. Find x.

Answer: 121°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 115 − 107 − 77 − 120 = 121
4.Each interior angle of a regular polygon is 160°. How many sides does it have?

Answer: 18

  1. Each exterior angle = 180° − 160° = 20°
  2. 360 ÷ 20 = 18 sides
5.The interior angles of a polygon add up to 2,520°. How many sides does it have?

Answer: 16

  1. (n − 2) × 180 = 2,520
  2. n − 2 = 2,520 ÷ 180 = 14, so n = 16
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 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 hexagon are 94°, 131°, 132°, 83°, 153° and x°. Find x.

Answer: 127°

  1. Angle sum = (6 − 2) × 180° = 720°
  2. x = 720 − 94 − 131 − 132 − 83 − 153 = 127
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 1,980°. How many sides does it have?

Answer: 13

  1. (n − 2) × 180 = 1,980
  2. n − 2 = 1,980 ÷ 180 = 11, so n = 13
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.