If ABCD is a cyclic quadrilateral in which AD||BC (fig. 16.180). Prove that ∠B=∠C.
Since, ABCD is a cyclic quadrilateral with AD ‖ BC
Then,
∠A + ∠C = 180o (i) (Opposite angles of cyclic quadrilateral)
And,
∠A + ∠B = 180o (ii) (Co. interior angles)
Comparing (i) and (ii), we get
∠B = ∠C
Hence, proved