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Mathematical proof angle
According to the meaning of the question, AB is parallel to CD, and the extension line DE makes PE and AB intersect at point E, then the angle CDP= angle AEP is known.

According to a triangle, the complementary angle of one angle is equal to the sum of the other two angles in the triangle, and the angle ABP- angle CDP= angle BPE= angle BPD.

The positions of AB and CD are interchanged as follows: Let the extension line BE make PE and CD intersect at point E, then the angle ABP= angle CEP is known.

According to a triangle, the complementary angle of one angle is equal to the sum of the other two angles in the triangle, and the angle CDP- angle ABP= angle BPE= angle BPD.