Year 8 Angles in Polygons Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 8 angles worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · AnglesYear 8 Angles in Polygons Worksheet — Level 1 — 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°
- Angle sum = (n − 2) × 180°
- (4 − 2) × 180° = 360°
2.Find the size of each interior angle of a regular octagon.
Answer: 135°
- Angle sum = (8 − 2) × 180° = 1,080°
- 1,080° ÷ 8 = 135°
3.Find the sum of the interior angles of a 20-sided polygon.
Answer: 3,240°
- Angle sum = (n − 2) × 180°
- (20 − 2) × 180° = 3,240°
4.Find the size of each interior angle of a regular triangle.
Answer: 60°
- Angle sum = (3 − 2) × 180° = 180°
- 180° ÷ 3 = 60°
5.Find the sum of the interior angles of a heptagon.
Answer: 900°
- Angle sum = (n − 2) × 180°
- (7 − 2) × 180° = 900°
6.Find the size of each interior angle of a regular 15-sided polygon.
Answer: 156°
- Angle sum = (15 − 2) × 180° = 2,340°
- 2,340° ÷ 15 = 156°
7.Find the sum of the interior angles of a 14-sided polygon.
Answer: 2,160°
- Angle sum = (n − 2) × 180°
- (14 − 2) × 180° = 2,160°
8.Find the size of each interior angle of a regular 24-sided polygon.
Answer: 165°
- Angle sum = (24 − 2) × 180° = 3,960°
- 3,960° ÷ 24 = 165°
9.Find the sum of the interior angles of a decagon.
Answer: 1,440°
- Angle sum = (n − 2) × 180°
- (10 − 2) × 180° = 1,440°
10.Find the size of each interior angle of a regular dodecagon.
Answer: 150°
- Angle sum = (12 − 2) × 180° = 1,800°
- 1,800° ÷ 12 = 150°
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.
Great work. Here's what to try next: