VTMO 2026 - Grade 8 - Semifinal - SET 3 - Self-study Question 20

In trapezoid $ABCD$, $AB\parallel CD$. Point $I$ is the midpoint of $DC$, $IH\perp AB$ with $H\in AB$, and $M,N$ are the midpoints of $AD,BC$. Given $IH=IM=IN=ID$, find $\angle DAB$.