Question

Observe the given construction, AF is the angular bisector of $\angle BAE$ and AC is the angular bisector of $\angle BAF$. 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 $\angle BAE$
$\Rightarrow \angle BAF=\frac{\angle BAE}{2}={30}^{\circ }$
and AC is angle bisector of $\angle BAF$
$\Rightarrow \angle BAC=\frac{\angle BAF}{2}={15}^{\circ }$