Day 20: Chase for the Angle

Geometry Level 3

In triangle $ABC$ , $BA=BC$ . The altitude $AD$ is drawn, then a point $P$ is selected on it. Let $E$ be the foot of the perpendicular of $AC$ from $P$ . $EP$ intersects $BC$ at $Q$ (both extended if necessary).

Given that $\angle ABC = 40^{\circ}$ , find the value of $\angle PQD$ .

This problem is part of the set Advent Calendar 2014.