Question
If $ABCD$ is a cyclic quadrilateral in which $AD\ ||\ BC$. Prove that $\angle\text{B}=\angle\text{C}.$ 
✓
Answer
Since, $ABCD$ is a cyclic quadrilateral with $AD\ ||\ BC$ Then,
$\angle\text{A}+\angle\text{C}=180^\circ\dots(1)$ [Opposite angles of cyclic quad.] And,
$\angle\text{A}+\angle\text{B}=180^\circ\dots(2)$ [Co-interior angles] Compare equations $(1)$ and $(2)$
$\angle\text{B}=\angle\text{C}$
$\angle\text{A}+\angle\text{C}=180^\circ\dots(1)$ [Opposite angles of cyclic quad.] And,
$\angle\text{A}+\angle\text{B}=180^\circ\dots(2)$ [Co-interior angles] Compare equations $(1)$ and $(2)$
$\angle\text{B}=\angle\text{C}$
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