Question

Observe the given construction, if $\angle BAE={60}^{\circ }$, then $\angle BAC$ will be

• A. ${60}^{\circ }$
• B. ${15}^{\circ }$
• C. ${30}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

The correct option is B

${15}^{\circ }$

$\angle BAE={60}^{\circ }$ [Given]
AF is angle bisector of $\angle BAE$
$\Rightarrow \angle BAF={\frac{60}{2}}^{\circ }$

= ${30}^{\circ }$
and AC is angle bisector of $\angle BAF$
$\Rightarrow \angle BAC={\frac{30}{2}}^{\circ }$ = ${15}^{\circ }$