In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (their sum is 180 degrees).
Given that the interior angle at point Y measures 30 degrees, the angle at point X, which is adjacent to angle Y, can be calculated as follows:
Angle X + Angle Y = 180 degrees
Angle X + 30 degrees = 180 degrees
Angle X = 180 degrees - 30 degrees
Angle X = 150 degrees
Therefore, the measure of the interior angle at point X is 150 degrees.