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