In a parallelogram, opposite angles are equal and adjacent angles are supplementary (they add up to 180 degrees).
Given that the interior angle at point Y measures 30 degrees, we can find the measure of the angle at point X. Since Y and X are adjacent angles in the parallelogram, we can write the equation:
\[ \text{Angle at Y} + \text{Angle at X} = 180^\circ \]
Substituting in the value we know:
\[ 30^\circ + \text{Angle at X} = 180^\circ \]
To find the angle at X, we subtract 30 degrees from 180 degrees:
\[ \text{Angle at X} = 180^\circ - 30^\circ = 150^\circ \]
Therefore, the measure of the interior angle at point X is 150 degrees.