RIOPLATENSE 2001 Problem 5

Let $ABC$ be a acute-angled triangle with centroid $G$ , the angle bisector of $\angle ABC$ intersects $AC$ in $D$ . Let $P$ and $Q$ be points in $BD$ where $\angle PBA = \angle PAB$ and $\angle QBC = \angle QCB$ . Let $M$ be the midpoint of $QP$ , let $N$ be a point in the line $GM$ such that $GN = 2GM$ (where $G$ is the segment $MN$ ), prove that: $\angle ANC + \angle ABC = 180$