The measure of ZRPQ is 130 degrees.
If RS is parallel to TU, and PT intersects RS at Q, then angles PRQ and QTU are corresponding angles. Corresponding angles are congruent when a transversal intersects two parallel lines.
Therefore, in this case, PRQ = QTU.
You mentioned that PRQ = 25 and QTU = 105, which means that both angles are equal. So, PRQ = QTU = 105 degrees.
Now, ZRPQ is an exterior angle formed by the transversal PT and the parallel lines RS and TU.
The measure of an exterior angle is equal to the sum of the measures of its corresponding interior angles.
Therefore, ZRPQ = PRQ + QTU = 25 + 105 = 130 degrees.
Hence, the measure of ZRPQ is 130 degrees.