Question

$ABCD$ is a cyclic quadrilateral. If $\angle A-\angle C={30}^{\circ }$, then $\angle C=$?

• A. ${90}^{\circ }$
• B. ${115}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

Answer: (D)

${75}^{\circ }$

Given, $ABCD$ is a cyclic quadrilateral.

We know, opposite angles of cyclic quadrilateral are supplementary.

Then, $\angle A+\angle C$$={180}^{\circ }$ .......(i).

But given, $\angle A-\angle C$$={30}^{\circ }$ .......(ii).

(i) $-$ (ii), we get,

$2\angle C={150}^o$

$⟹$ $\angle C={75}^o$.

Hence, option $C$ is correct.