Angles (Including Parallel Lines): WJEC GCSE Foundation November 2017 Unit 1 Q18

Foundation November 2017 Unit 1 Q18

WJECFoundationCurrent spec5 marksAngles (Including Parallel Lines)Angles in Polygons

18. ABCD is a quadrilateral.
\(A\hat{B}C\) = 93°, \(B\hat{C}D\) = 122° and \(A\hat{D}C\) = 85°.
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 degrees, angle C = 122 degrees and angle B = 93 degrees; Q on AD and P on AB 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.
(\(B\hat{A}D\) =) 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.