2011 HMMT November General Round Problem 2

Let ABC be a triangle, and let D, E, and F be the midpoints of sides BC, CA, and AB, respectively. Let the angle bisectors of \angle FDE and \angle FBD meet at P. Given that \angle BAC = 37^\circ and \angle CBA = 85^\circ, determine the degree measure of \angle BPD.

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2011 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.