Question

For the following figure, find the value of $x$.

Short answer

The value of$x={45}^{\circ }$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangles.

An isosceles triangle is a triangle that has two sides of equal length and two equal angles.

Step 3. Find the value.

Since the triangle is isosceles triangles thus $AB=AC$and $\angle ABC={90}^{\circ }$.

$\angle BAC=\angle BAC=x^{\circ }$.

Therefore, find the value of $x$as follows:

$$\begin{gathered} \angle ABC+\angle ACB+\angle BAC={180}^{\circ } \\ {90}^{\circ }+x+x={180}^{\circ } \\ 2x={180}^{\circ }-{90}^{\circ } \\ x={45}^{\circ } \end{gathered}$$

Therefore, the value of $x={45}^{\circ }$.