A point $P$ is marked within regular hexagon $ABCDEF$ so that we have $\angle BAP=\angle DCP = 50^\circ $ If $\angle APB$ has measure $x$ degrees, find $x$.
Here's a diagram:
Referring to the diagram, I've tried to do some angle chasing:
$\angle PAF=\angle PGE=\angle CPH=\angle PCB=70, \angle PGF=110, \angle GPA=HPC=60$, and all the interior angles are equal to $120$.
However, it seems like this isn't sufficient to solve the problem and I think I might need a construction of some sort - but I'm stuck here.
Assuming the solution needs more than just angle chasing, I'd appreciate constructions/observations and explanations of why they'd solve the problem.