Question
Look at this diagram:
Q
R
S
T
U
V
W
X
If
RT
and
UW
are parallel lines and mTSV= 132°, what is mUVS?
Q
R
S
T
U
V
W
X
If
RT
and
UW
are parallel lines and mTSV= 132°, what is mUVS?
Answers
GPT-4o mini
To find \( mUVS \), let's analyze the diagram based on what we know.
Given that \( RT \) and \( UW \) are parallel lines and \( mTSV = 132^\circ \), we can identify the relationships involving angles formed by these parallel lines and the transversal.
1. **Identify the transversal**: The line that intersects both parallel lines \( RT \) and \( UW \) creates angles on both lines.
2. **Find the corresponding angles**: Since \( RT \) is parallel to \( UW \), the angles formed in the same positions (corresponding angles) are equal.
**From the information given**:
- \( mTSV = 132^\circ \): This represents the angle formed at the intersection of the transversal on line \( RT \).
- The corresponding angle \( mUVS \) on the line \( UW \) (since \( UVS \) corresponds to \( TSV \)) will also be equal to \( mTSV \).
Thus,
\[
mUVS = mTSV = 132^\circ
\]
Therefore, \( mUVS = 132^\circ \).
Given that \( RT \) and \( UW \) are parallel lines and \( mTSV = 132^\circ \), we can identify the relationships involving angles formed by these parallel lines and the transversal.
1. **Identify the transversal**: The line that intersects both parallel lines \( RT \) and \( UW \) creates angles on both lines.
2. **Find the corresponding angles**: Since \( RT \) is parallel to \( UW \), the angles formed in the same positions (corresponding angles) are equal.
**From the information given**:
- \( mTSV = 132^\circ \): This represents the angle formed at the intersection of the transversal on line \( RT \).
- The corresponding angle \( mUVS \) on the line \( UW \) (since \( UVS \) corresponds to \( TSV \)) will also be equal to \( mTSV \).
Thus,
\[
mUVS = mTSV = 132^\circ
\]
Therefore, \( mUVS = 132^\circ \).