Question

In an equilateral triangle ΔABC, AE is the angle bisector of ∠A, then the measure of ∠BAE is degrees.

Answer 1

$\underset{–}{\text{Given:}}$
$\bullet$ $△ABC$ is an equilateral triangle
$\bullet$ $AE$ is the angle bisector of $\angle A$

Let us draw a figure using the given informations:
$\angle BAE$ and $\angle CAE$ combine to from $\angle BAC$.
$\therefore m\angle BAE+m\angle CAE=m\angle BAC$
AE is the angle bisector, i.e.
$m\angle BAE=m\angle CAE$
$\therefore m\angle BAE+m\angle BAE=m\angle BAC$
$\Rightarrow 2m\angle BAE=m\angle BAC$

Now, each of the three angles of an equilateral triangle measures ${60}^o$.
$\therefore m\angle BAC={60}^o$

Combining both the equations,
$2m\angle BAE$ $=$ ${60}^o$
Dividing both sides by $2$,
$\Rightarrow \frac{2m\angle BAE}{2}=\frac{{60}^o}{2}$
$\Rightarrow$ m$\angle BAE={30}^o$