4MA0 Higher June 2016 Paper 4R Q4

EdexcelHigherOld spec7 marksAngles (Including Parallel Lines)Angles in Polygons

4 Here is a kite \(ABCD\).

Kite ABCD with angle DAB = 111° and right angle at D

Diagram NOT accurately drawn

Angle \(DAB\) = 111°
Angle \(ADC\) = 90°

(a) Work out the size of angle \(ABC\). (2)

Two of these kites are arranged so that a shorter side of one of the kites is placed on top of a shorter side of the other kite, as shown in the diagram below.

Two of the kites placed with a shorter side of one on a shorter side of the other, with angles x and y marked

Diagram NOT accurately drawn

(b) Work out the size of angle \(x\). (2)

Scheme	Marks
360 − 2 × 111 − 90	M1
48	A1
	(2)

Scheme	Marks
111 − 90	M1
21	A1
	(2)

Mark scheme (c)

Scheme	Marks
540 − 90 − 90 − 111 – 111 or 180 – 2 × ‘21’ or 2 × (180 – 111) or 360 − 111 = 249 180 − (360 – ‘21’ −249 − 48) oe	M2
138	A1
	(3)

Notes

M2: For a fully correct method to find angle \(y\) or M1 if using pentagon for (5−2)×180 (=540) or for an isosceles triangle drawn with \(y\) at apex or for showing use of parallel lines on diagram