Angles and Quadrilaterals Problem 70

Question

In a quadrilateral FGHI, FG = GI, ∠GFI = 70, ∠GHI = 55 and FI is parallel to GH. What is the size of ∠GFH? I thought it would be 50. Is that correct?

Answer 1

I got $\measuredangle GFH=35^{\circ}$.

$\measuredangle FIH=180^{\circ}-55^{\circ}=125^{\circ}$ and since $GF=GI$, we obtain $\measuredangle GIH=125^{\circ}-70^{\circ}=55^{\circ}$,

which says $GH=GI=GF$, which gives that $FH$ is a bisector of $\angle GFH$

and from here we obtain: $\measuredangle GFH=35^{\circ}$.