Given, ABCD is a quadrilateral in which AB || DC and AD = BC.
Extend AB to E and draw a line CE parallel to AD.
Since AD||CE and transversal AE cuts them at A and E, respectively.
∠A + ∠E = 180
∠A = 180-∠E
Since, AB||CD and AD||CE
So quadrilateral AECD is a parallelogram.
Now, AD = CE BC = CE
CE = BC
∠CBE = ∠CEB (opposite angles of equal sides are equal)
180-∠B = ∠E
180-∠E = ∠B
∠A = ∠B
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