To find the measure of angle \( mVUW \), we can use the properties of parallel lines and transversal angles.
Given that \( QS \) and \( TV \) are parallel lines, and \( mSRU = 47^\circ \):
- The angle \( SRU \) is an interior angle on the same side of the transversal.
By the Corresponding Angles Postulate, we know that when two parallel lines are cut by a transversal, the angles that are in corresponding positions are equal. Therefore, since \( mSRU \) and \( mVUW \) are corresponding angles, we have:
\[ mVUW = mSRU = 47^\circ \]
Thus, the measure of angle \( mVUW \) is \( 47^\circ \).