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