To solve for \( m TUW \), we can use the properties of parallel lines and angles. Given that \( QS \) and \( TV \) are parallel lines, several angle relationships apply.
Given:
- \( m SRP = 120^\circ \)
Since \( SRP \) and \( TUW \) are corresponding angles (formed by the transversal that intersects the parallel lines \( QS \) and \( TV \)), we know:
\[ m TUW = m SRP \]
Thus, we can conclude:
\[ m TUW = 120^\circ \]
So the measure of angle \( TUW \) is \( 120^\circ \).