Question

Quadilateral ABCD is cyclic. If $\angle B={60}^o$, then $\angle D=$____.

• A. ${30}^o$
• B. ${100}^o$
• C. ${120}^o$
• D. ${90}^o$

Answer 1

Answer: (C)

${120}^o$

In a cyclic quadrilateral, the sum of opposite angles $={180}^{\circ }$.

Given, $ABCD$ is a cyclic quadrilateral.

Then, $\angle B$ and $\angle D$ are opposite angles

Hence $\angle B+\angle D={180}^{\circ }$

$\Rightarrow \angle D={180}^{\circ }-\angle B$

$\Rightarrow \angle D={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

Therefore, $\angle D={120}^{\circ }$.

Thus, option $C$ is correct.