Geometry Essentials · Challenge problem

Roads $\ell$ and $m$ are parallel, with $\ell$ to the north of $m$. A path runs from a point $A$ on $\ell$ to a point $P$ between the roads, making a $38^\circ$ angle with $\ell$, then continues from $P$ to a point $B$ on $m$, making a $52^\circ$ angle with $m$. Points $A$ and $B$ are on the same side of $P$ (both to the east). Find $m\angle APB$.