4MA1/1HR Jun 2023, Question 15: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
Hexagon BCDEFG has angles 57°, 104°, 149°, 95° and a right angle at B; AB, BC, CD are sides of a regular n-gon. Find n, showing working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Angles in a hexagon add to (6 − 2) × 180 = 720°.
- 2Reflex angle BCD = 720 − (90 + 57 + 104 + 149 + 95) = 225°.
- 3Interior angle of the polygon at C = 360 − 225 = 135°.
- 4Exterior angle = 180 − 135 = 45°.
- 5n = 360 ÷ 45 = 8
Answer8
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