Question

Solve for x and y in the problem below. Then, find m

Answer 1

Given the Cyclic Quadrilateral Theorem,

Opposite angles of a Cyclic Quadrilateral are supplementary(that is, they add up to 180°).

Therefore,

`\begin{gathered} 17x+78^o=180^o \\ 17x=180^o-78^o \\ 17x=102^o \\ x=(102^o)/(17) \\ x=6^o \end{gathered}`

To obtain y,

`\begin{gathered} 9y+6y=180^o \\ 15y=180^o \\ y=(180^o)/(15) \\ y=12^o \end{gathered}`

Thus,

`\begin{gathered} m\angle X=9y \\ =9*12 \\ =108^o \end{gathered}`
`\begin{gathered} m\angle V=6y \\ =6*12 \\ =72^o \end{gathered}`
`\begin{gathered} m\angle W=17x \\ =17*6 \\ =102^o \end{gathered}`

Therefore, the values are

m

m

m