Success TutoringWorksheets

Year 8 Angles in Polygons Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 angles worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Angles

Year 8 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 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 pentagon are 107°, 81°, 107°, 125° and x°. Find x.

Answer: 120°

  1. Angle sum = (5 − 2) × 180° = 540°
  2. x = 540 − 107 − 81 − 107 − 125 = 120
4.Each interior angle of a regular polygon is 156°. How many sides does it have?

Answer: 15

  1. Each exterior angle = 180° − 156° = 24°
  2. 360 ÷ 24 = 15 sides
5.The interior angles of a polygon add up to 1,800°. How many sides does it have?

Answer: 12

  1. (n − 2) × 180 = 1,800
  2. n − 2 = 1,800 ÷ 180 = 10, so n = 12
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 20°. How many sides does it have?

Answer: 18

  1. Exterior angles add to 360°
  2. 360 ÷ 20 = 18 sides
8.The interior angles of a heptagon are 124°, 142°, 128°, 147°, 107°, 80° and x°. Find x.

Answer: 172°

  1. Angle sum = (7 − 2) × 180° = 900°
  2. x = 900 − 124 − 142 − 128 − 147 − 107 − 80 = 172
9.Each interior angle of a regular polygon is 120°. How many sides does it have?

Answer: 6

  1. Each exterior angle = 180° − 120° = 60°
  2. 360 ÷ 60 = 6 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.