4MA1/2H Nov 2021, Question 5: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Find the marked angle x between a regular octagon and a pentagon sharing side DH, given three pentagon angles and that angle GHD equals angle FGH. Show your working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Pentagon angles add to (5 − 2) × 180 = 540°
- 2540 − 112 − 102 − 96 = 230, so angle GHD = 230 ÷ 2 = 115°
- 3Octagon interior angle = (8 − 2) × 180 ÷ 8 = 135°
- 4Angles at H: x = 360 − 115 − 135 = 110°
Answer110
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