4MA1/2H Jun 2018, Question 12: 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
Hexagon ABCDEF has BC parallel to ED, with angles FAB = 96°, ABC = 144°, BCD = 42° and EFA = 50°. Find the obtuse angle DEF.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1BC ∥ ED, so angle CDE = 180° − 42° = 138° (co-interior angles)
- 2Angles in a hexagon add up to (6 − 2) × 180° = 720°
- 3Reflex angle DEF = 720 − (96 + 144 + 42 + 138 + 50) = 720 − 470 = 250°
- 4Obtuse angle DEF = 360° − 250° = 110
Answer110
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