The problem asks to find the value of $x$ in the given diagram, where two parallel lines are intersected by a transversal. One angle is given as $56^{\circ}$.

1. Problem Description

The problem asks to find the value of $x$ in the given diagram, where two parallel lines are intersected by a transversal. One angle is given as $56^{\circ}$.

2. Solution Steps

Since the two lines are parallel, and are intersected by a transversal line, we can use the properties of angles formed by parallel lines and a transversal. The angle marked $56^{\circ}$ and the angle $x$ are alternate interior angles. Alternate interior angles are supplementary only when the transversal crosses one of the parallel lines in a perpendicular manner. Here, we see that the transversal line does not cross the parallel lines at right angles.

Let us look at the supplementary angle of $56^{\circ}$, call it $y$. Thus we have

$y + 56^{\circ} = 180^{\circ}$.

$y = 180^{\circ} - 56^{\circ} = 124^{\circ}$.

The angle $y$ and $x$ are corresponding angles, hence $y = x$.

$x = 124^{\circ}$

3. Final Answer

124