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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