Look at this diagram:

Question

Q
R
S
T
U
V
W
X




























If
RT
and
UW
are parallel lines and
m
UVX
= 53°, what is
m
RSV
?

Answer 1

To find the measure of angle \( mRSV \), we can use the properties of parallel lines and angles.

Given that \( RT \) and \( UW \) are parallel lines and \( mUVX = 53° \), we can determine the relationship between angles formed by a transversal that crosses these parallel lines.

Since \( UV \) acts as a transversal to the parallel lines \( RT \) and \( UW \), we can determine the corresponding or alternate interior angles.

1. Identify angles:

   • \( mUVX \) is given as \( 53° \).
   • \( RSV \) is the angle adjacent to \( UVX \) along line \( UW \).

2. Find angle:

   • The angle \( RSV \) is an alternate interior angle to \( UVX \) because \( RT \) and \( UW \) are parallel.
   • Since \( UVX = 53° \), and the corresponding angle \( RSV \) (due to the parallel line property) is equal to \( UVX \), we have: \[ mRSV = mUVX = 53° \]

Therefore, the measure of angle \( mRSV \) is \( \boxed{53°} \).