Foundation June 2022 Paper 3 Q20
20 In the diagram, \(PQR\) is an isosceles triangle with \(PQ = PR\).

\(APR\) 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)
| 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.