Question

In the adjoining figure if BO and CO are the bisectors of $\angle EBC\&\angle DCB$ respectively the value of $\angle BOC$ is

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${30}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

$\angle BAC+\angle ABC=60+70=130$
$\angle ACB=180-\angle BAC+\angle ABC=180-130=50$
$\angle EBC=180-70=110$
$\angle DCB=180-50=130$
$\angle OBC=\frac{1}{2}\angle DCB=\frac{130}{2}=65$
$\angle CBO=\frac{1}{2}\angle EBC=\frac{110}{2}=55$
$\angle OBC=180-65-55=60$