Find the angle

Geometry Level 4

Let \(D\) be the point on the base \(BC\) of an isosceles triangle \(ABC\) with \(AB=AC\) and \(m(BAC)=80^\circ\), such that \(BD : DC = 2 : 1\), and let \(P\) be the point on the segment \(AD\) such that \(m(BAC) = m(BPD)\). Find \(m(DPC)\) in degrees.

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