Question

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

Short answer

The value of$x={80}^{\circ }$.

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 $\angle BAC=x$.

$\angle ABC=\angle ACB={50}^{\circ }$

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

$$\begin{gathered} \angle ABC+\angle ACB+\angle BAC={180}^{\circ } \\ {50}^{\circ }+{50}^{\circ }+x={180}^{\circ } \\ x={180}^{\circ }-{100}^{\circ } \\ x={80}^{\circ } \end{gathered}$$

Therefore, the value of $x={80}^{\circ }$.