From the figure, notice that the triangles IJK and IHK are congruent for the HL criterion.
On the other hand, the angles HIK and JIK are congruent since they are opposed to sides of equal length, and they are corresponding angles from the congruence statement.
Then, the measure of those angles must be the same:
[tex]3v=v+8[/tex]Solve for v:
[tex]\begin{gathered} \Rightarrow3v-v=8 \\ \Rightarrow2v=8 \\ \Rightarrow v=\frac{8}{2} \\ \therefore v=4 \end{gathered}[/tex]Therefore:
[tex]v=4[/tex]