Problem

Source: Tuymaada 2003, day 1, problem 2.

Tags: trigonometry, geometry, perpendicular bisector, geometry proposed



In a quadrilateral $ABCD$ sides $AB$ and $CD$ are equal, $\angle A=150^\circ,$ $\angle B=44^\circ,$ $\angle C=72^\circ.$ Perpendicular bisector of the segment $AD$ meets the side $BC$ at point $P.$ Find $\angle APD.$ Proposed by F. Bakharev