In general,
[tex]Inscribed\text{ angle}=\frac{1}{2}\text{ Intercepted Arc}[/tex]In our case, notice that both [tex]\begin{gathered} \angle y=\angle w=\frac{1}{2}*108\degree=54\degree \\ \Rightarrow\angle y=\angle w=54\degree \end{gathered}[/tex]Similarly, [tex]\begin{gathered} \angle x=\angle z=\frac{1}{2}*40\degree=20\degree \\ \Rightarrow\angle x=\angle z=20\degree \end{gathered}[/tex]Thus, the answer is x=20