Question

find the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(y\). So, \(y+39^{\circ}+85^{\circ}=180^{\circ}\).

Step2: Solve for the third - interior angle \(y\)

\[

$$\begin{align*} y&=180^{\circ}-(39^{\circ} + 85^{\circ})\\ y&=180^{\circ}-124^{\circ}\\ y& = 56^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

The angle \(x\) and the third - interior angle \(y\) form a linear pair. Since the sum of angles in a linear pair is 180°, then \(x + y=180^{\circ}\). Substituting \(y = 56^{\circ}\), we get \(x=180^{\circ}-56^{\circ}\).

Step4: Calculate the value of \(x\)

\[x = 124^{\circ}\]

Answer:

\(124^{\circ}\)