In a parallelogram, opposite angles are equal, and the sum of the interior angles in any quadrilateral is 360 degrees. Given that the interior angle at point Y measures 30 degrees, the opposite angle at point W will also measure 30 degrees.
To find the angle at point X, we can use the fact that consecutive angles in a parallelogram are supplementary (they add up to 180 degrees). Therefore, we can calculate angle X as follows:
\[ \text{Angle at X} + \text{Angle at Y} = 180^\circ \] \[ \text{Angle at X} + 30^\circ = 180^\circ \] \[ \text{Angle at X} = 180^\circ - 30^\circ = 150^\circ \]
Thus, the measure of the interior angle at point X is 150 degrees.