Finding Angle θ in Parallelogram ABCD

[utkarshakash]

Homework Statement

In the parallelogram ABCD the internal bisectors of the consecutive angles B and C intersect at P. Use vector method to find angle BPC.

Homework Equations

The Attempt at a Solution

I assume angle BPC to be θ and the point of intersection of internal bisectors to be P. But what is the next operation which I should use? I tried taking dot product of PB and PC but I don't yet know the magnitudes of both vectors.

 

[haruspex]

Invent some vector variables to represent, say, CD and CB. What vector represents the direction of the bisector of BCD? How about that of ABC?