# 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.

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