4MA0 Foundation June 2013 Paper 1 Q11

Diagram NOT accurately drawn

In triangle \(ABD\), \(AB = AD = BD\).
In triangle \(BCD\), angle \(BDC = 65^\circ\) and \(BC = BD\).

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

(4)

Mark scheme

Scheme	Marks
\(\angle ABD = 60^\circ\) or \(\angle BAD = 60^\circ\) or \(\angle ADB = 60^\circ\) or \(180 \div 3\)	M1
\(\angle BCD = 65^\circ\) or \((\angle CBD =)\; 180 - 2 \times 65\)	M1
\((\angle CBD =)\; 50^\circ\)	A1
\(\angle ABC = 60^\circ + 50^\circ\) Answer: 110	A1
	(4)

M1: Angles may be unambiguously stated eg \(C\) or \(A\) but \(ABD\) etc or marked on diagram.

A1: Award 4 marks for an answer of 110