4MA1/2HR Jan 2023, Question 11: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Use the given straight lines and parallel lines with angles 128° and 32° to work out how many sides the regular polygon has; show your working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1RST is parallel to CD, so angle SCD = angle RSC = 128° (alternate angles)
- 2SCU and BCV are straight lines, so angle BCS = angle UCV = 32° (vertically opposite angles)
- 3Interior angle BCD = 128° + 32° = 160°
- 4Sum of the interior angles of an n-sided polygon = (n − 2) × 180
- 5160n = (n − 2) × 180
- 6160n = 180n − 360
- 720n = 360
- 8n = 18
- 9The polygon has 18 sides
Answer18
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