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0580/43 Oct/Nov 2025, Question 5: Interior and Exterior Angles of Polygons

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 4 marks

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The question, in short

Find the angle d at a vertex of a regular decagon between a line of symmetry and a side, then find n for a regular polygon with exterior angle 45°.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Work out the value of d, the angle at A between the line of symmetry AB and a side of the regular decagon.

  1. 1Exterior angle = 360 ÷ 10 = 36°
  2. 2Interior angle = 180 − 36 = 144°
  3. 3AB is a line of symmetry so it bisects the angle at A
  4. 4d = 144 ÷ 2 = 72

Answer72

Part (b) · 1 mark

Work out the value of n for a regular polygon whose exterior angle is 45°.

  1. 1n = 360 ÷ 45
  2. 2n = 8

Answer8

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Also searched as: 0580/43/O/N/25 · 0580_w25_qp_43 · 0580 w25 43 · question 5.
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