Question
Look at this diagram:
P
Q
R
S
T
U
V
W
If
QS
and
TV
are parallel lines and mVUW= 66°, what is mQRP?
P
Q
R
S
T
U
V
W
If
QS
and
TV
are parallel lines and mVUW= 66°, what is mQRP?
Answers
GPT-4o mini
To find the measure of angle \( mQRP \), we need to analyze the information given in the problem regarding parallel lines and the angles formed by a transversal.
Given that \( QS \) and \( TV \) are parallel lines and \( mVUW = 66^\circ \), we need to identify the relationship between \( mVUW \) and \( mQRP \).
Since \( QS \) and \( TV \) are parallel lines, and if we assume that \( UW \) is a transversal cutting across both parallel lines, we can use the concept of corresponding angles.
- \( VUW \) and \( QRP \) (which can be presumed to be the angle formed at point \( R \), between lines \( QS \) and \( UW \)) are corresponding angles due to the parallel nature of \( QS \) and \( TV \).
- Since corresponding angles are equal when lines are parallel, we have:
\[
mQRP = mVUW
\]
Thus, substituting the value given in the problem:
\[
mQRP = 66^\circ
\]
Therefore, the measure of angle \( mQRP \) is \( \boxed{66^\circ} \).
Given that \( QS \) and \( TV \) are parallel lines and \( mVUW = 66^\circ \), we need to identify the relationship between \( mVUW \) and \( mQRP \).
Since \( QS \) and \( TV \) are parallel lines, and if we assume that \( UW \) is a transversal cutting across both parallel lines, we can use the concept of corresponding angles.
- \( VUW \) and \( QRP \) (which can be presumed to be the angle formed at point \( R \), between lines \( QS \) and \( UW \)) are corresponding angles due to the parallel nature of \( QS \) and \( TV \).
- Since corresponding angles are equal when lines are parallel, we have:
\[
mQRP = mVUW
\]
Thus, substituting the value given in the problem:
\[
mQRP = 66^\circ
\]
Therefore, the measure of angle \( mQRP \) is \( \boxed{66^\circ} \).