Question

In the given figure $ABCD$ is a cyclic quadrilateral and $AD=BC$. If $\angle A={110}^{\circ }$, then find $\angle B$

• A. ${70}^{\circ }$
• B. ${80}^{\circ }$
• C. ${100}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

Answer: (D)

${110}^{\circ }$

Opposite angle in a Cyclic Quadrilateral are Supplementary (Sum=${180}^o$)

$\therefore \angle A+\angle C={180}^o\Rightarrow \angle C={70}^o$

Since, AD=BC and they have DC line in common so, $\angle D={70}^o$

and since, ${70}^o+\angle B={180}^o\Rightarrow \angle B={110}^o$

Hence, the answer is ${110}^o$