Given:
Consider the three point of second line are S, R, V instead of S, R, W.
A line with points T, R, W intersects a line with points S, R, V at point R. Another line extends from point R to point U between angle T, R, V.
![\angle VRW=(3x)^\circ](https://tex.z-dn.net/?f=%5Cangle%20VRW%3D%283x%29%5E%5Ccirc)
![\angle TRS=(2x+18)^\circ](https://tex.z-dn.net/?f=%5Cangle%20TRS%3D%282x%2B18%29%5E%5Ccirc)
To find:
The m∠SRW.
Solution:
The figure according to the given information is shown below (not to scale).
From the below figure it is clear that,
and
are vertically opposite angles. So, their measures are equal.
![3x=2x+18](https://tex.z-dn.net/?f=3x%3D2x%2B18)
Subtract 2x from both sides.
![3x-2x=18](https://tex.z-dn.net/?f=3x-2x%3D18)
![x=18](https://tex.z-dn.net/?f=x%3D18)
Using x=18 the measure of angle VRW is
![\angle VRW=(3x)^\circ](https://tex.z-dn.net/?f=%5Cangle%20VRW%3D%283x%29%5E%5Ccirc)
![\angle VRW=(3\times 18)^\circ](https://tex.z-dn.net/?f=%5Cangle%20VRW%3D%283%5Ctimes%2018%29%5E%5Ccirc)
![\angle VRW=54^\circ](https://tex.z-dn.net/?f=%5Cangle%20VRW%3D54%5E%5Ccirc)
Now,
[Linear pair]
![54^\circ+\angle SRW=180^\circ](https://tex.z-dn.net/?f=54%5E%5Ccirc%2B%5Cangle%20SRW%3D180%5E%5Ccirc)
![\angle SRW=180^\circ-54^\circ](https://tex.z-dn.net/?f=%5Cangle%20SRW%3D180%5E%5Ccirc-54%5E%5Ccirc)
![\angle SRW=126^\circ](https://tex.z-dn.net/?f=%5Cangle%20SRW%3D126%5E%5Ccirc)
Therefore, the correct option is C.