To solve for \( mUTQ \), we need to use the property of angles formed by parallel lines intersected by a transversal.
Given that \( PR \) and \( SU \) are parallel lines, and \( QT \) is a transversal intersecting them, the angles \( RQT \) and \( UTQ \) are alternate interior angles.
According to the properties of parallel lines:
\[ mRQT = mUTQ \]
Since you've mentioned that \( mRQT = 55^\circ \), we have:
\[ mUTQ = 55^\circ \]
Thus, the measure of angle \( UTQ \) is \( 55^\circ \).