COMC 2023 B Problem 4

Consider triangle A B C with angles \angle B A C=24^{\circ} and \angle A C B=28^{\circ}. Point D is constructed such that A B is parallel to C D, A D=B C, and A D and B C are not parallel. Similarly, point E is constructed such that A E is parallel to B C, A B=C E, and A B and C E are not parallel. Lines D E and A C intersect at point P. Determine angle \angle C P E (in degrees).