QuintinD579771 QuintinD579771
  • 03-11-2022
  • Mathematics
contestada

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

Find the value of X and each arc measurex mGKmHJ mHGJ mGKJ class=

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TamilaM286449 TamilaM286449
  • 03-11-2022
[tex]m\angle GK+m\angle GH+m\angle HJ+m\angle KJ=360[/tex]

where:

[tex]\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}[/tex]

add like terms:

[tex]14x+66=360[/tex]

Solve for x:

[tex]\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=\frac{294}{14} \\ x=21 \end{gathered}[/tex]

Hence:

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

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