Question

In the given figure, $BD=DC$ and $\angle DBC={30}^{\circ }$ what is the value of $\angle BAC$?

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

Answer: (C)

${60}^{\circ }$

As $BD=DC$ ...... (given)

$\Rightarrow \angle DBC=\angle DCB={30}^{\circ }$

$\Rightarrow \angle BDC={180}^{\circ }-{30}^{\circ }-{30}^{\circ }={120}^{\circ }$

As $ABCD$ is a cyclic quadrilateral ; $\angle BAC+\angle BDC={180}^{\circ }$

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