4MA1/2F Jun 2023, Question 27: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 3 marks
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The question, in short
A regular 9-sided polygon ABCDEFGHJ has centre O; OD and FE are extended to meet at K. Find the value of angle x at K.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Exterior angle = 360 ÷ 9 = 40°, so interior angle = 140°
- 2OD bisects the angle at D, so angle ODE = 70° and angle EDK = 180 − 70 = 110°
- 3FEK is straight, so angle DEK = exterior angle = 40°
- 4x = 180 − 110 − 40 = 30
Answer30
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