Olympiad Geometry · Hard problem

Parallel lines $\ell$ and $m$ are cut by a transversal. Where the transversal crosses $\ell$, one acute angle measures $(x + 4y)^\circ$ and the obtuse angle adjacent to it measures $(5x + 2y)^\circ$. Where the transversal crosses $m$, the angle corresponding to the $(x + 4y)^\circ$ angle measures $(3x + 2y)^\circ$. Find the measure of the obtuse angle.