Question

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

Short answer

The value of$x=5$.

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$\angle ABC=\angle ACB={40}^{\circ }$ and $AB=AC$.

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

$\begin{array}{c}AB=AC\\ 5x-8=2x+7\\ 5x-2x=7+8\\ x=5\end{array}$

Therefore, the value of $x=5$.