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 ${60}^{\circ }$
$\Rightarrow \angle BAF={30}^{\circ }$
and AC is angle bisector of ${30}^{\circ }$
$\Rightarrow \angle BAC={15}^{\circ }$