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:

$\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=\frac{294}{14} \\ x=21 \end{gathered}$

Hence:

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