In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (meaning they add up to 180 degrees). Given that the interior angle at point Y measures 30 degrees, you can find the measure of the angle at point X as follows:
Since angles Y and X are consecutive angles, we have:
\[ \text{Angle Y} + \text{Angle X} = 180^\circ \]
Substituting the value of angle Y:
\[ 30^\circ + \text{Angle X} = 180^\circ \]
Now, solve for angle X:
\[ \text{Angle X} = 180^\circ - 30^\circ = 150^\circ \]
Therefore, the measure of the interior angle at point X is \(150\) degrees.
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