Angles in Polygons: WJEC GCSE Intermediate November 2017 Unit 1 Q7

Intermediate November 2017 Unit 1 Q7

WJECIntermediateCurrent spec5 marksAngles in Polygons

7. \(ABCD\) is a quadrilateral.
\(A\hat{B}C = 93^\circ\), \(B\hat{C}D = 122^\circ\) and \(A\hat{D}C = 85^\circ\).
Points \(P\) and \(Q\) lie on the quadrilateral as shown, such that \(AP = AQ\).

Prove that triangle \(APQ\) is an equilateral triangle.
You must show all your working. [5]

Quadrilateral ABCD with angle D = 85°, angle C = 122°, angle B = 93°; P on AB and Q on AD joined by a dashed line.

Diagram not drawn to scale

Mark scheme

Scheme	Marks	Comments
		This is a ‘proof’ question so the work for the M1 mark must be seen before the A1 mark can be awarded.
(BÂD =) 360 – ( 85 + 122 + 93)	M1
= 60(°)	A1
(APQ = AQP = ) \(\dfrac{180 - 60}{2}\)	M1	F.T. ‘their 60’ only if previous M1 awarded. Allow reference to isosceles triangle.
= 60(°)	A1
A convincing statement AND the three angles shown as, or stated to be 60(°)	E1	Independent of previous marks. Must refer to three (all) angles being equal. Three angles of 60° must be shown or stated as part of a convincing statement. Reference to equal sides alone is E0.