4MA1/2H Jan 2022, Question 11: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
For a regular 10-sided polygon ABCDEFGHIJ with diagonals AG and AD drawn, show that the angle JAG equals the angle GAD.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Exterior angle = 360 ÷ 10 = 36°, so interior angle = 180 − 36 = 144°
- 2Pentagon GHIJA has angle sum 540°; angles H, I, J give 3 × 144 = 432°
- 3Angles at G and A are equal, so x = (540 − 432) ÷ 2 = 54
- 4In ABCD, angle BAD = (360 − 2 × 144) ÷ 2 = 36
- 5Angle JAB = 144, so y = 144 − 54 − 36 = 54, giving x = 54, y = 54
Answerx = 54, y = 54
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