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4024/12 Oct/Nov 2022, Question 7: Interior and Exterior Angles of Polygons

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Using a diagram of part of a regular pentagon with AB parallel to DC, find the angles x at B and y at C.

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

Part (a) · 2 marks

Find the value of angle x at vertex B.

  1. 1Interior angle of a regular pentagon = 180 × (5 − 2) ÷ 5
  2. 2= 540 ÷ 5 = 108
  3. 3x = 108

Answer108

Part (b) · 1 mark

Find the value of angle y at vertex C.

  1. 1AB is parallel to DC, so angles ABC and BCD are co-interior
  2. 2y = 180 − 108 = 72

Answer72

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