0580/31 Oct/Nov 2025, Question 20: Interior and Exterior Angles of Polygons
Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 4 marks
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The question, in short
Calculate the interior angle of a regular 8-sided polygon, then use a circle diagram with diameter AB, tangent DBE at B and angle CBA = 71° to find x, giving a reason.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Find the size of a single interior angle in a regular polygon with 8 sides.
- 1Exterior angle = 360 ÷ 8 = 45°
- 2Interior angle = 180 − 45 = 135°
Answer135
Part (b) · 2 marks
Using the circle with diameter AB, tangent DBE at B and angle CBA = 71°, determine x and state a geometrical reason.
- 1Angle ABD = 90° because the angle between a tangent and a radius is 90°
- 2x = 90 − 71 = 19
Answer19 Angle between tangent and radius = 90
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Also searched as: 0580/31/O/N/25 · 0580_w25_qp_31 · 0580 w25 31 · question 20.
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