We are given two parallel lines intersected by a transversal. One angle is given as $133^{\circ}$, and we need to find the value of angle $x$.

1. Problem Description

We are given two parallel lines intersected by a transversal. One angle is given as $133^{\circ}$, and we need to find the value of angle $x$.

2. Solution Steps

Since the two lines are parallel, the angle given ($133^{\circ}$) and the angle adjacent to $x$ on the same transversal are supplementary angles. Let's call the angle adjacent to $x$ as $y$.

$133^{\circ} + y = 180^{\circ}$

$y = 180^{\circ} - 133^{\circ}$

$y = 47^{\circ}$

The angles $x$ and $y$ are vertical angles. Therefore, they are equal.

$x = y$

$x = 47^{\circ}$

3. Final Answer

$x = 47^{\circ}$