Let BAC be Ф. in ABC, B = C as isosceles Δ.
ABC = BCA = (180 - Ф)/2 = 90-Ф/2
As AB parallel to CD, BAC = ACD = Ф.
Also ACB = CAD = 90 - Ф/2
In ΔCAD, ADC = 180 - ACD - CAD = 180 - Ф - 90 + Ф/2 = 90 -Ф/2
So ADC = ABC.
Opposite angles are same and two sides are parallel, it is a parallelogram