4MA1/2F Nov 2021, Question 21: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 5 marks
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The question, in short
Find the angle x at H between a regular octagon and a pentagon sharing side DH, given pentagon angles 112°, 102°, 96° and angle GHD equals angle FGH.
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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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