Given the Cyclic Quadrilateral Theorem,
Opposite angles of a Cyclic Quadrilateral are supplementary(that is, they add up to 180°).
Therefore,
[tex]\begin{gathered} 17x+78^o=180^o \\ 17x=180^o-78^o \\ 17x=102^o \\ x=\frac{102^o}{17} \\ x=6^o \end{gathered}[/tex]
To obtain y,
[tex]\begin{gathered} 9y+6y=180^o \\ 15y=180^o \\ y=\frac{180^o}{15} \\ y=12^o \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} m\angle X=9y \\ =9\times12 \\ =108^o \end{gathered}[/tex][tex]\begin{gathered} m\angle V=6y \\ =6\times12 \\ =72^o \end{gathered}[/tex][tex]\begin{gathered} m\angle W=17x \\ =17\times6 \\ =102^o \end{gathered}[/tex]
Therefore, the values are
m
m
m
