Let ABCD be a cyclic parallelogram.
∠A + ∠C = 180° (Opposite angles of a cyclic quadrilateral) ... (1)
We know that opposite angles of a parallelogram are equal.
∠A = ∠C and ∠B = ∠D
From equation (1),
∠A + ∠C = 180°
∠A + ∠A = 180°
2 ∠A = 180°
∠A = 90°
Parallelogram ABCD has one of its interior angles as 90°. Therefore, it is a rectangle.