4MA1/2FR Jan 2022, Question 21: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 4 marks
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The question, in short
Using the regular octagon ABCDEFGH and regular pentagon ABIJK sharing side AB, calculate the size of angle x at I, between IB and the dashed line IC.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Octagon interior angle ABC = 180 − 360 ÷ 8 = 135°
- 2Pentagon interior angle ABI = 180 − 360 ÷ 5 = 108°
- 3Angle IBC = 135 − 108 = 27°
- 4BI = BA = BC, so triangle IBC is isosceles
- 5x = (180 − 27) ÷ 2 = 76.5
Answer76.5
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