Question

Find the value of x.

Short answer

The value of$x$ is $\mathbf{30}\mathbf{°}$.

Step-by-step solution

Step 1. Name the given figure.

Step 2. Description of step.

Consider$\mathrm{\Delta }ABC$ from the given figure it can be observed that, $\overline{AB}\cong \overline{AC}$. It implies that$\mathrm{\Delta }ABC$ is an isosceles triangle. Therefore,

$\angle ABC\cong \angle ACB$

Step 3. Description of step.

If two lines are intersected by transversal then the angle formed by transversal with respect to two lines are equal.

Here,$\overline{DE}\left|\right|\overline{BC}$ which implies that$\angle ABC=\angle BAD$ and $\angle ACB=\angle CAE$.

Therefore, $\angle BAD=\angle CAE$.

Step 4. Description of step.

Substitute $2x$for $\angle BAD$and $90-x$for $\angle CAE$into the equation obtained in step 3.

$$\begin{gathered} 2x=90-x \\ 3x=90 \\ x=30 \end{gathered}$$

Therefore, the value of $x$is $30°$.