How do I solve the missing verticals angles for L2 and L3?

The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:
Then, if we apply this theorem to the figure shown we can say that
[tex]\begin{gathered} L1=L3 \\ L2=L4 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} L2=110.6 \\ L3=69.4 \end{gathered}[/tex]