Question

Look at this diagram:

P
Q
R
S
T
U
V
W


If
QS
and
TV
are parallel lines and mSRU= 122°, what is mQRP?

Answer 1

To find the measure of angle \( mQRP \), given that \( QS \) and \( TV \) are parallel lines and \( mSRU = 122^\circ \), we can use the properties of parallel lines and transversals.

Since \( QS \) and \( TV \) are parallel, the angles formed by a transversal crossing these parallel lines have specific relationships.

1. **Identifying the Transversal**:
The segment \( SRU \) can be seen as a transversal intersecting the parallel lines \( QS \) and \( TV \).

2. **Using the Angles**:
The angle \( mSRU \) (which is \( 122^\circ \)) is an interior angle on the same side of the transversal as \( mQRP \). By the Consecutive Interior Angles Theorem, we know that the sum of these angles is \( 180^\circ \) because they are on the same side of the transversal between the parallel lines.

Thus, we can set up the equation:
\[
mQRP + mSRU = 180^\circ
\]

Substituting the value we know:
\[
mQRP + 122^\circ = 180^\circ
\]

3. **Solving for \( mQRP \)**:
\[
mQRP = 180^\circ - 122^\circ
\]
\[
mQRP = 58^\circ
\]

Therefore, the measure of angle \( mQRP \) is \( 58^\circ \).