Middle European Mathematical Olympiad 2009 Problem I-3

Let $ABCD$ be a convex quadrilateral such that $AB$ and $CD$ are not parallel and $AB = CD$. The midpoints of the diagonals $AC$ and $BD$ are $E$ and $F$. The line $EF$ meets segments $AB$ and $CD$ at $G$ and $H$, respectively. Show that $\measuredangle AGH = \measuredangle DHG$.