0580/22 Feb/Mar 2025, Question 10: Interior and Exterior Angles of Polygons
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 5 marks
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The question, in short
Use three regular polygons meeting at a point with interior angles in ratio 3:4:5 to show polygon C has twice the sides of B.
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Solution · 5 marks
- 1Angles at a point add to 360°, and 3 + 4 + 5 = 12 parts
- 2One part = 360 ÷ 12 = 30°, so b = 4 × 30 = 120° and c = 5 × 30 = 150°
- 3B: exterior angle = 180 − 120 = 60°, sides = 360 ÷ 60 = 6
- 4C: exterior angle = 180 − 150 = 30°, sides = 360 ÷ 30 = 12
- 5So B has 6 sides and C has 12 sides, 12 = 2 × 6
AnswerB has 6 sides and C has 12 sides, 12 = 2 × 6
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