We have two triangle UTS, and WXV, they are simillar because all of their angles are equal. This is demonstrated by the fact the angle U and W are:
[tex]\begin{gathered} \measuredangle U=180-67-54=59 \\ \measuredangle W=180-54-59=67 \end{gathered}[/tex]
This means that every corresponding sides of the triangles are related by the same constant. We can use this fact to calculate VW, as shown below:
[tex]\begin{gathered} \frac{VW}{WX}=\frac{ST}{TU} \\ \frac{VW}{51}=\frac{107}{102} \\ VW=\frac{51\cdot107}{102} \\ VW=53.5 \end{gathered}[/tex]
The side VW has a length of 53.5
