Find the angle

Geometry Level 4

Let DD be the point on the base BCBC of an isosceles triangle ABCABC with AB=ACAB=AC and m(BAC)=80m(BAC)=80^\circ, such that BD:DC=2:1BD : DC = 2 : 1, and let PP be the point on the segment ADAD such that m(BAC)=m(BPD)m(BAC) = m(BPD). Find m(DPC)m(DPC) in degrees.

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