Question

Please solve quickly and give solution before hand if possible

Answer 1

In general,

`Inscribed\text{ angle}=(1)/(2)\text{ Intercepted Arc}`

In our case, notice that both
`\begin{gathered} \angle y=\angle w=(1)/(2)*108\degree=54\degree \\ \Rightarrow\angle y=\angle w=54\degree \end{gathered}`Similarly,
`\begin{gathered} \angle x=\angle z=(1)/(2)*40\degree=20\degree \\ \Rightarrow\angle x=\angle z=20\degree \end{gathered}`Thus, the answer is x=20