Question

Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠ BAF. If ∠BAE = 60°, then find the value of ∠BAC.

Answer 1

Given : : ∠BAE = 60°
$\because$ AF is an angle bisector of $\angle$BAE
$\Rightarrow \angle BAF=\frac{1}{2}\angle BAE\Rightarrow \angle BAF=\frac{1}{2}\times {60}^{\circ }={30}^{\circ }$
From the above result,
$\angle BAF={30}^{\circ }$
But AC is angle bisector of $\angle BAF$
$\Rightarrow \angle BAC=\frac{1}{2}\angle BAF\Rightarrow \angle BAC=\frac{1}{2}\times {30}^{\circ }={15}^{\circ }$