UA-UMO 2005 Problem 107

A point $M$ is taken on the perpendicular bisector of the side $AC$ of an acute-angled triangle $ABC$ so that $M$ and $B$ are on the same side of $AC$ . If $\angle BAC=\angle MCB$ and $\angle ABC+\angle MBC=180^{\circ}$ , find $\angle BAC.$