Question

hallar el valor de 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, \(y+34^{\circ}+86^{\circ}=180^{\circ}\).

Step2: Solve for \(y\)

\[

$$\begin{align*} y&=180^{\circ}-(34^{\circ} + 86^{\circ})\\ y&=180^{\circ}-120^{\circ}\\ y& = 60^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

Since \(x\) and \(y\) form a linear pair (a straight - line angle is 180°), then \(x + y=180^{\circ}\). Substitute \(y = 60^{\circ}\) into the equation.
\[

$$\begin{align*} x&=180^{\circ}-y\\ x&=180^{\circ}-60^{\circ}\\ x&=120^{\circ} \end{align*}$$

\]

Answer:

\(120^{\circ}\)