Question

Find the measure of $\angle BAE$ in the following figure.

• A. ${30}^{\circ }$
• B. ${15}^{\circ }$
• C. ${45}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${15}^{\circ }$

$\angle ABC={90}^{\circ }$ [Angle of a square]

Also, $\angle EBC={60}^{\circ }$ [Angle of an equilateral triangle]

So, $\angle ABE=\angle ABC+\angle EBC={90}^{\circ }+{60}^{\circ }={150}^{\circ }$

In $\Delta ABE$, BE = AB [Given]

That means $\Delta ABE$ is isosceles.

Let $\angle BEA=\angle BAE=x$

$x+x+\angle ABE={180}^{\circ }$ [Angle sum property]

$2x={180}^{\circ }-{150}^{\circ }={30}^{\circ }$

$x={15}^{\circ }$

So, $\angle BEA=\angle BAE={15}^{\circ }$