0580/32 Oct/Nov 2021, Question 4: Angles in Parallel Lines
Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks
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The question, in short
Use parallel lines and triangle angle facts to find x, y, z; find angle u in a circle with centre O; calculate the perimeter of a sector with radius 6.42 cm and angle 72°.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
With DAE parallel to FBCG, use angle EAC = 73° and angle ABC = 58° to find x, y and z in triangle ABC.
- 1x = 180 − 58 = 122 (angles on a straight line)
- 2y = 73 (alternate angles, angle ACB = angle EAC)
- 3z = 180 − 58 − 73 = 49 (angles in a triangle)
- 4x = 122, y = 73, z = 49
Answerx = 122, y = 73, z = 49
Part (b) · 2 marks
For points P, Q, R on a circle centre O with PR a diameter and angle QRP = 32°, find angle u, QPR.
- 1PR is a diameter, so angle PQR = 90° (angle in a semicircle)
- 2u = 180 − 90 − 32 = 58
Answer58
Part (c) · 3 marks
Find the perimeter of a sector of radius 6.42 cm and sector angle 72°, including the two radii and arc.
- 1Arc = 72/360 × 2 × π × 6.42 = 8.06… cm
- 2Perimeter = 8.06… + 2 × 6.42 = 20.90… ≈ 20.9 cm
Answer20.9 or 20.90 to 20.91
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Also searched as: 0580/32/O/N/21 · 0580_w21_qp_32 · 0580 w21 32 · question 4.
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