0580/22 Oct/Nov 2025, Question 16: Interior and Exterior Angles of Polygons
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks
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The question, in short
Two regular polygons share side AB; BD and BC are other sides meeting at B with angle DBC = 14°. Find n, the number of sides of the polygon containing AB and BC.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Exterior angle of 15-sided polygon = 360 ÷ 15 = 24°
- 2Exterior angle of n-sided polygon = 24 − 14 = 10°
- 3n = 360 ÷ 10 = 36
Answer36
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