Question

If PR and SU are parallel lines and mUTV = 67°, what is mPQO? °

Answer 1

To find the measure of angle \( mPQO \), let's analyze the situation given that lines \( PR \) and \( SU \) are parallel, and angle \( mUTV = 67^\circ \).

Since \( PR \) and \( SU \) are parallel, we can deduce relationships between angles formed by a transversal intersecting these lines. The measure \( mUTV \) being \( 67^\circ \) implies there is a certain angle configuration involving angles created by the transversal.

1. If \( U \) is on line \( PR \) and \( T \) and \( V \) are on line \( SU \), then \( \angle UTV \) could relate to others:
- If angles \( UTV \) and \( PQO \) are corresponding angles (same relative position at each intersection with the transversal), then:
\[
mPQO = mUTV = 67^\circ.
\]
- If \( mUTV \) and \( mPQO \) are alternate interior angles or another type of angle pair, the value might still be \( 67^\circ \).

Given that the problem suggests a parallel line scenario and doesn't specify angle relationships beyond \( mUTV \), it is most reasonable to conclude:

\[
mPQO = 67^\circ.
\]

Thus, the measure of \( mPQO \) is \( 67^\circ \).