Question

Find the measure of $\angle DAE$ in the figure below.

• A. ${30}^{\circ }$
• B. ${25}^{\circ }$
• C. $5^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is D

${15}^{\circ }$

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

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

So, $\angle ABE=\angle ABC-\angle EBC={90}^{\circ }-{60}^{\circ }={30}^{\circ }$

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]

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

$x={75}^{\circ }$

So, $\angle BEA=\angle BAE={75}^{\circ }$

Now, $\angle DAE=\angle DAB-\angle BAE={90}^{\circ }-{75}^{\circ }={15}^{\circ }$