We are given a diagram with two intersecting lines and two parallel lines. One angle is labeled as $138^\circ$ and another angle is labeled as $x$. We need to find the value of $x$.

1. Problem Description

We are given a diagram with two intersecting lines and two parallel lines. One angle is labeled as $138^\circ$ and another angle is labeled as $x$. We need to find the value of $x$.

2. Solution Steps

First, consider the angle that is $138^\circ$. Its supplementary angle, let's call it $y$, lies on the same straight line, therefore their sum is $180^\circ$.

$$y + 138^\circ = 180^\circ$$

$$y = 180^\circ - 138^\circ$$

$$y = 42^\circ$$

Since the lines are parallel, the angle $x$ is equal to the angle $y$. This is because they are corresponding angles.

Therefore, $x = y = 42^\circ$.

3. Final Answer

$x = 42^\circ$