4MA1/1F Jun 2022, Question 19: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks
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The question, in short
Three regular polygons A, B and C meet at a point with interior angles 8x°, 7x° and 3x°. Polygon B has n sides; work out n.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1The three angles meet at a point, so 8x + 7x + 3x = 360
- 218x = 360, so x = 20
- 3Polygon B is the one marked 7x°, so its interior angle is 7 × 20 = 140°
- 4The exterior angle is 180 − 140 = 40°
- 5The exterior angles of a regular polygon add to 360°, so n = 360 ÷ 40
- 6n = 9
Answer9
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