Question

$\text{In the given figure BD = DC and}\angle CBD={30}^{\circ }\text{Find}\left(\angle BAC\right)$

• A. ${60}^{\circ }$
• B. ${80}^{\circ }$
• C. ${30}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$

Given, BD=DC
$\therefore \angle BCD=\angle CBD={30}^{\circ }$
So, $\angle BDC=180-30-30={120}^{\circ }$
$\because$ ABCD is cyclic
$\therefore \angle BAC=180-120={60}^{\circ }$