Foundation June 2022 Paper 3 Q20

EdexcelCurrent spec5 marksAngles (Including Parallel Lines)

20 In the diagram, \(PQR\) is an isosceles triangle with \(PQ = PR\).

Isosceles triangle PQR with P at the top and QR horizontal; line APR extends through P to A, line BPQ extends through P to B, angle APB is 56 degrees; line CQD passes through Q parallel to APR, with arrows marking the parallel lines

\(APR\) and \(CQD\) are parallel lines.
\(BPQ\) is a straight line.

Angle \(APB = 56^\circ\)

Work out the size of angle \(CQR\).
Give a reason for each stage of your working. (5)

Mark scheme

Answer	Mark	Mark scheme
118 with reasons	M1	for angle \(QPR = 56\) or \(CQP = 56\)
	M1	for angle \(PQR = (180 - 56) \div 2\ (= 62)\)
	C1	(dep on a previous M1) for giving a reason relating to parallel lines: angle \(CQR = 180 - \text{``}62\text{''}\) (Allied angles / Co-interior angles add up to 180) or angle \(CQP = 56\) (corresponding angles are equal) or use “angle \(QPR\)” (alternate angles are equal)
	C1	(dep on a previous M1) for at least one reason given from: vertically opposite angles are equal OR vertically opposite angles are equal or base angles of an isosceles triangle are equal or Angles in a triangle add up to 180
	A1	for 118

Additional guidance

Angles must be clearly labelled on the diagram or otherwise identified.
Full solution must be seen.
Correct method can be implied from angles on the diagram if no ambiguity or contradiction.

When reasons are given the key words underlined must be present.
Reasons need to be linked to their method; any reasons not linked, do not credit. There should be no incorrect reasons given.