The total circunference of a circle is 360º. Then, the sum of the arcs in the given circle sum 36º:
[tex]\text{mGJ}+\text{mJI}+\text{mIH}+mHG=360º[/tex][tex](x+58)+(x-23)+(x-23)+(x+48)=360[/tex]
Solve the equation for x:
[tex]\begin{gathered} x+58+x-23+x-23+x+48=360 \\ 4x+60=360 \\ 4x+60-60=360-60 \\ 4x=300 \\ \frac{4}{4}x=\frac{300}{4} \\ \\ x=75 \end{gathered}[/tex]
Use the value of x to find the measure of arc GJ:
[tex]\text{mGJ}=x+58=75+58=133º[/tex]The measure of arc GJ is 133º
