To find the measure of the exterior angle \( x \), we can use the property that the exterior angle of a polygon is equal to the sum of the two opposite interior angles. The exterior angle and the adjacent interior angle also sum up to 180 degrees.
Given that one interior angle is \( 40 \) degrees and we consider it adjacent to the exterior angle \( x \), we can use the formula:
\[ x + 40 = 180 \]
Now, we solve for \( x \):
\[ x = 180 - 40 \] \[ x = 140 \text{ degrees} \]
Therefore, the measure of the exterior angle \( x \) is \( 140 \) degrees.