Look at this diagram:

Question

O
P
Q
R
S
T
U
V




























If
PR
and
SU
are parallel lines and
m
RQT
= 42°, what is
m
UTQ
?

Answer 1

To find the measure of angle \( m \angle UTQ \), we can utilize the properties of parallel lines and the angles formed by a transversal.

Given that lines \( PR \) and \( SU \) are parallel and \( m \angle RQT = 42^\circ \), we can refer to the diagram context where \( QT \) is a transversal that intersects both parallel lines.

Since \( PR \) and \( SU \) are parallel, the angles \( RQT \) and \( UTQ \) are corresponding angles. Corresponding angles are equal when two lines are crossed by a transversal.

Thus, we have: \[ m \angle UTQ = m \angle RQT = 42^\circ \]

Therefore, the measure of angle \( UTQ \) is: \[ \boxed{42^\circ} \]