Construct a line which passes through P and parallel to AD, it cuts AB and CD at X, Y, similarly for ZT. $ \Delta DZP\sim \Delta BXP \Rightarrow \frac{PZ}{PX}=\frac{DZ}{BX} \Rightarrow \frac{PZ}{AZ}=\frac{PY}{CY}$ $ \Rightarrow \Delta AZP\sim \Delta CYP \Rightarrow \angle PAD=\angle PCD$ Similarly, $ \angle QAD=\angle QCD$ $ \Rightarrow \angle PAQ=\angle PCQ$

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