Question

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

Short answer

The value of$x=11$.

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.

From the figure,$AC=10,BC=11,\angle BAC={63}^{\circ },\angle ABC={54}^{\circ }$ and $AB=x$.

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

$$\begin{gathered} \angle ABC+\angle ACB+\angle BAC={180}^{\circ } \\ {54}^{\circ }+{63}^{\circ }+\angle ACB={180}^{\circ } \\ \angle ACB={63}^{\circ } \end{gathered}$$

Since the triangle is isosceles triangle then$\angle ACB=\angle BAC={63}^{\circ }$ and $AB=BC=11$.

Therefore, the value of $x=11$.