We are given a diagram with two parallel lines intersected by a transversal. One angle is labeled as $82^{\circ}$, 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 parallel lines intersected by a transversal. One angle is labeled as $82^{\circ}$, and another angle is labeled as $x$. We need to find the value of $x$.

2. Solution Steps

The $82^{\circ}$ angle and the angle $x$ are consecutive interior angles.

Consecutive interior angles are supplementary, meaning their sum is $180^{\circ}$.

Therefore, we can write the equation:

$x + 82^{\circ} = 180^{\circ}$

Subtracting $82^{\circ}$ from both sides, we get:

$x = 180^{\circ} - 82^{\circ}$

$x = 98^{\circ}$

3. Final Answer

$x = 98^{\circ}$