Question 103
Let $M$ and $N$ be points on side $BC$ of triangle $ABC$ such that $BM = CN$, with $M$ in the interior of segment $BN$. Let $P, Q$ be points on segments $AN$ and $AM$ respectively such that $\angle PMC = \angle MAB$ and $\angle QNB = \angle NAC$. Is it true that $\angle QBC = \angle PCB$?