In convex quadrilateral \(A B C D, A B=C D, \angle A B C=77^{\circ},\) and \(\angle B C D=150^{\circ} .\) Let P be the intersection of the perpendicular bisectors of \(\overline{B C}\) and \(\overline{A D}\). Find \(\angle P B C\) and \(\angle BPC\).