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∠ACB+ ∠ABC= ∠CAP ( exterior angle is equal to sum of opp. interior angles)
so, ∠CAP= 2 ∠ACB =2ABC
∠CAP= 2∠CAD= 2∠DAP
so, ∠ACB=∠CAD 
but they are alt interior angles
so, AD parallel to DC

hence ABCD is a parallelogram
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