4MA1/1HR Jan 2021, Question 8: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Use the regular pentagon ABCDE and regular hexagon CFGHID with straight lines AEJ and HIJ to work out the size of angle x, showing clear working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Pentagon interior angle = 3 × 180 ÷ 5 = 108°; hexagon = 4 × 180 ÷ 6 = 120°
- 2Angles at D: angle EDI = 360 − 108 − 120 = 132°
- 3Straight lines: angle DEJ = 180 − 108 = 72° and angle DIJ = 180 − 120 = 60°
- 4Quadrilateral EDIJ angles add to 360°: x = 360 − 132 − 72 − 60 = 96
Answer96
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