Foundation November 2020 Paper 2 Q18

EdexcelCurrent spec5 marksAngles (Including Parallel Lines)

Parallelogram ABCD with angle BCD = 58°; CD is extended to F and AD is extended to E, forming triangle DEF with DE = DF marked equal; angle DEF is marked

Diagram NOT accurately drawn

The diagram shows a parallelogram \(ABCD\) and an isosceles triangle \(DEF\) in which \(DE = DF\)

\(CDF\) and \(ADE\) are straight lines.
Angle \(BCD = 58°\)

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

(5)

Mark scheme

Scheme	Marks
\(ADC\) = 180 – 58 (= 122) or \(EDF\) = 122 or \(CDE\) = 58 or \(ADF\) = 58	M1
e.g. \(DEF\) = 58 ÷ 2 or \(DEF\) = (180 – 122) ÷ 2	M1
Working required Answer: 29	A1
	B2
	(5)
	(5 marks)

Notes

M1: may be seen marked on the diagram

M1: complete method to find angle \(DEF\)

B2: dep on M2 for fully correct reasons for their method (B1 dep on M1 for one correct reason stated and used) e.g.
Allied angles, co-interior angles, Alternate angles, Corresponding angles, Vertically opposite angles are equal (or Vertically opposite angles are equal), Angles on a straight line add up to 180° (or angles on a straight line add to 180°), Sum of two angles in a triangle are equal to opposite exterior angle, Angles in a triangle add up to 180° (or Angles in a triangle add up to 180°), Base angles in an isosceles triangle
Angles in a quadrilateral add up to 360. (accept “4-sided shape” or parallelogram)
Opposite angles of a parallelogram are equal