We are given two parallel lines intersected by a transversal. One angle is labeled as $122^{\circ}$, and another angle is labeled as $x$. We need to find the value of $x$.

1. Problem Description

We are given two parallel lines intersected by a transversal. One angle is labeled as $122^{\circ}$, and another angle is labeled as $x$. We need to find the value of $x$.

2. Solution Steps

Since the two horizontal lines are parallel, the angle labeled $122^{\circ}$ and the angle adjacent to $x$ that is on the same line form same-side interior angles. Same-side interior angles are supplementary, which means they add up to $180^{\circ}$. Let the angle adjacent to $x$ be $y$.

$122^{\circ} + y = 180^{\circ}$

$y = 180^{\circ} - 122^{\circ}$

$y = 58^{\circ}$

Angles $x$ and $y$ are vertical angles, which means they are equal.

$x = y$

$x = 58^{\circ}$

3. Final Answer

58