Foundation June 2019 Paper 1 Q8

EdexcelFoundationCurrent spec5 marksAngles (Including Parallel Lines)

8 The diagram shows two triangles, \(CDB\) and \(BDA\).

Triangles CDB and BDA sharing side DB; A is above B and C is to the left of B with a right angle at B; angle DAB is 55 degrees, angle CDB is 116 degrees, DC and DB are marked equal, and the reflex angle ADC at D is marked x

Diagram NOT accurately drawn

\(DC = DB\)
Angle \(ABC = 90^\circ\)
Angle \(CDB = 116^\circ\)
Angle \(DAB = 55^\circ\)

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

(5)

Mark scheme

Scheme	Marks
angle \(DBC\) (or \(DCB\)) = (180 – 116) ÷ 2 (=32)	M1
angle \(ADB\) = 180 – (90 –“32”) – 55 (=67) or angle \(ADB\) = 360 – 116 – “32” – 55 – 90 (=67)	M1
\(x\) = 360 – 116 – “67” (= 177)	M1
177 with reasons	A2
	(5)
	(5 marks)

Notes

M1: angles may be seen on diagram

M1: dep

A2: for 177 and full reasons
base angles in an isosceles triangle are equal
angles in a triangle add up to 180°
angles at a point add up to 360°

If not A2 then A1 for 177 with 1 correct reason

(SCB1 dep on M1 for a correct reason explicitly linked to their correct method)

(corrected from the printed mark scheme: the first line prints “angle \(DBC\) (or \(DBC\))”; the other base angle is \(DCB\).)