Higher June 2019 Paper 1R Q23

EdexcelHigherCurrent spec4 marksCircle Theorems

Circle through B, C, D and F; lines ABC and AFD meet at A with angle 54°, lines BFE and CDE meet at E with angle 32°, and angle x is marked at B between BC and BF

Diagram NOT accurately drawn

\(B\), \(C\), \(D\) and \(F\) are points on a circle.
\(ABC\), \(AFD\), \(BFE\) and \(CDE\) are straight lines.
Work out the size of angle \(x\).
Show your working clearly.

(4)

Mark scheme

Scheme	Marks
\(ABF = 180 - x\) or \(CDF = 180 - x\)	M1
\(FDE = 180 - (180 - x)\) (\(= x\)) \(AFB\) or \(ACE = 180 - (180 - x) - 54\) (\(= x - 54\)) \(DFE\) or \(ACE = 180 - x - 32\) (\(= 148 - x\)) e.g. \(54 + y + 180 - x = 180\) where \(AFB = y\) \(32 + y + (180 - (180 - x)) = 180\) where \(DFE = y\)	M1
e.g. \(32 + x + x - 54 = 180\) or \(54 + 180 - x + 148 - x = 180\) or \(x - 54 = 148 - x\) oe or \(54 + y + 180 - x = 180\) and \(32 + y + (180 - (180 - x)) = 180\) where \(AFB = DFE = y\)	M1
Working required Answer: 101	A1
	(4)
	(4 marks)

Notes

M1: for finding an expression for \(ABF\) or \(CDF\).
May be seen on diagram.

M1: method to find \(FDE\) and \(AFB\)
or method to find \(FDE\) and \(DFE\)
or method to find \(ACE\)
or method to find \(FDE\) and an equation for \(AFB\) e.g. \(54 + y + 180 - x = 180\) where \(AFB = y\)
or method to find \(FDE\) and an equation for \(DFE\) e.g. \(32 + y + (180 - (180 - x)) = 180\) where \(DFE = y\)
May be seen on diagram.

M1: for setting up an equation or a pair of correct simultaneous equations to solve for \(x\)

A1: dep on at least M1