0580/42 Feb/Mar 2021, Question 3: Angles in Parallel Lines
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks
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The question, in short
Use the parallel-line angle diagram to work out a, b and c, then use circle theorems in two separate circle diagrams to find x and y.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
From the diagram of two parallel lines crossed by two straight lines, determine the sizes of angles a, b and c.
- 1a = 126 (vertically opposite angles)
- 2b = 180 − 126 = 54 (co-interior angles)
- 3c = 180 − 63 = 117 (co-interior angles)
Answera = 126, b = 54, c = 117
Part (b) · 3 marks
With R and S on a circle having diameter PQ and RQ parallel to PS, angle RPQ = 58°, calculate x and justify each step geometrically.
- 1Angle PRQ = 90° (angle in a semicircle)
- 2Angle RPS + angle PRQ = 180° (co-interior angles, RQ parallel to PS)
- 358 + x + 90 = 180
- 4x = 32
Answer32
Part (c) · 2 marks
For points A, B and C on a circle with centre O and angle AOC = 142°, work out the size of angle y.
- 1Reflex angle AOC = 360 − 142 = 218°
- 2Angle at circumference is half angle at centre
- 3y = 218 ÷ 2 = 109
Answer109
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Also searched as: 0580/42/F/M/21 · 0580_m21_qp_42 · 0580 m21 42 · question 3.
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