Question

Find the value of X and each arc measurex =mGK=mHJ = mHGJ =mGKJ=

Answer 1

`m\angle GK+m\angle GH+m\angle HJ+m\angle KJ=360`

where:

`\begin{gathered} m\angle GK=9x-22 \\ m\angle GH=61 \\ m\angle HJ=5x-7 \\ m\angle KJ=34 \\ so\colon \\ 9x-22+61+5x-7+34=360 \\ \end{gathered}`

add like terms:

`14x+66=360`

Solve for x:

`\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=(294)/(14) \\ x=21 \end{gathered}`

Hence:

`\begin{gathered} m\angle GK=9x-22=9(21)-22=167 \\ m\angle HJ=5x-7=5(21)-7=98 \end{gathered}`