0580/21 Oct/Nov 2022, Question 16: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks
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The question, in short
Using the circle diagram with eight chords and marked angles 20°, 72° and 56°, work out the sizes of the angles u, v, w and x.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1u = 20 (angles in the same segment)
- 2Exterior angle of triangle: angle at top-left point = 56 − 20 = 36, so x = 36 (angles in the same segment)
- 3Triangle with 72° and 56°: 180 − 72 − 56 = 52, so v = 52 (angles in the same segment)
- 4w = 180 − 72 = 108 (opposite angles of a cyclic quadrilateral)
Answeru = 20, v = 52, w = 108, x = 36
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Also searched as: 0580/21/O/N/22 · 0580_w22_qp_21 · 0580 w22 21 · question 16.
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