Question

If ABCD is a cyclic quadrilateral in which $AD||BC$. Prove that $\angle B=\angle C$.

Answer 1

Given : ABCD is a cyclic quadrilateral in which (AD || BC)

To prove : $\angle B=\angle C$

Proof : $\because AD||BC$

$\therefore \angle A+\angle B={180}^{\circ }$ (Sum of cointerior angles)

But $\angle A+\angle C={180}^{\circ }$ (Opposite angles of the cyclic quadrilateral)

$\therefore \angle A+\angle B=\angle A+\angle C$

$\Rightarrow \angle B=\angle C$

Hence, proved.