Prove that a cyclic parallelogram is always a rectangle

To prove that a llgm is a rectangle we need to prove that any one angle is 90.

Given: ABCD is a cyclic llgm
To prove : ABCD is a rectangle
Proof : 

angle A = angle C(opposite angles of llgm are equal)

angle A angle C = 180 (sum of opposite angles of cyclic quadrilateral is 180)

2angle of A = 180
Angle A = 90

Since, ABCD is a llgm and one angle is 90. So, ABCD is a rectangle.

Hence Proved.