In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to 180 degrees).
Given that the interior angle at point Y is 30 degrees, the angle at point X, which is consecutive to Y, can be calculated as follows:
\[ \text{Angle at } X = 180^\circ - \text{Angle at } Y = 180^\circ - 30^\circ = 150^\circ \]
Therefore, the measure of the interior angle at point X is 150 degrees.
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