Note that angle GPF = angle BPC since they are congruent angles. so GPF = 22

since AD is perpendicular to CG, angle APG = 90

since PE bisects DPF, we have angle FPE = angle DPE, so we can write,

APG + DPE = DPE + DPE = 2DPE

now, A and D are colinear, so the su of the angles on one side of AD add up to 180 degrees, that is,

angleAPG + angleGPF + 2*angleDPE = 180

=> 90 + 22 + 2DPE = 180

=> 2DPE = 180 - 90 - 22 = 68

=> DPE = 68/2 = 34 degrees