In a parallelogram, opposite angles are equal and consecutive angles are supplementary (i.e., they add up to 180 degrees).
Given that the angle at point Y is 30 degrees, we can find the measure of the angle at point X:
Angle W + Angle Y = 180 degrees
Since angle Y is 30 degrees: Angle W + 30 degrees = 180 degrees
Thus, Angle W = 180 degrees - 30 degrees = 150 degrees.
Since W and X are opposite angles in the parallelogram, angle X will also equal angle W:
Angle X = 150 degrees.
So, the measure of the interior angle at point X is 150 degrees.