We are given a diagram with two parallel lines $PQ$ and $SR$. We are given an exterior angle of $246^{\circ}$ and an interior angle of $68^{\circ}$. We are asked to find the value of the angle $x^{\circ}$.

1. Problem Description

We are given a diagram with two parallel lines $PQ$ and $SR$. We are given an exterior angle of $246^{\circ}$ and an interior angle of $68^{\circ}$. We are asked to find the value of the angle $x^{\circ}$.

2. Solution Steps

First, find the interior angle adjacent to the exterior angle of $246^{\circ}$. The sum of these two angles is $360^{\circ}$. Let this interior angle be $y$.

$y + 246^{\circ} = 360^{\circ}$

$y = 360^{\circ} - 246^{\circ}$

$y = 114^{\circ}$

Now, we have a transversal cutting through two parallel lines $PQ$ and $SR$. The two interior angles on the same side of the transversal are supplementary. That means they add up to $180^{\circ}$. Let the angle vertically opposite to the $68^{\circ}$ angle be $68^{\circ}$.

Then we have the interior angle on the same side of the transversal as the $68^{\circ}$ angle as $114^{\circ}$.

Consider the triangle. The angles of the triangle are $x$, $68$, and $180 - 114 = 66$.

The sum of the angles in a triangle is $180^{\circ}$.

$x + 68^{\circ} + (180^{\circ} - 114^{\circ}) = 180^{\circ}$

$x + 68^{\circ} + 66^{\circ} = 180^{\circ}$

$x + 134^{\circ} = 180^{\circ}$

$x = 180^{\circ} - 134^{\circ}$

$x = 46^{\circ}$

3. Final Answer

The value of $x$ is

4

6. Final Answer: B