Question

what is the value of x?

Explanation:

Step1: Find the vertical - angle

The angle vertical to the $158^{\circ}$ angle is also $158^{\circ}$ since vertical angles are equal.

Step2: Use the exterior - angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the triangle be $\triangle LMN$. The exterior angle is $158^{\circ}$, and the two non - adjacent interior angles are $x^{\circ}$ and $68^{\circ}$. So, $158=x + 68$.

Step3: Solve for $x$

Subtract $68$ from both sides of the equation $158=x + 68$. We get $x=158 - 68$.
$x = 90$

Answer:

$90$