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UKMT Pink Kangaroo, 2017

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows a triangle $FHI$ , and a point $G$ on $FH$ such that $GH = FI$ . The points $M$ and $N$ are the midpoints of $FG$ and $HI$ respectively. Angle $NMH = \alpha°$ . Which of the following gives an expression for $\angle IFH$ ?

(A) $2\alpha°$ (B) $(90-\alpha)°$ (C) $45+\alpha°$ (D) $(90-\frac{1}{2}\alpha)°$ (E) $60°$

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