Question

What is mGJ? G X +480 X+580 H J X-23° X-239 I

Answer 1

The total circunference of a circle is 360º. Then, the sum of the arcs in the given circle sum 36º:

`\text{mGJ}+\text{mJI}+\text{mIH}+mHG=360º`
`(x+58)+(x-23)+(x-23)+(x+48)=360`

Solve the equation for x:

`\begin{gathered} x+58+x-23+x-23+x+48=360 \\ 4x+60=360 \\ 4x+60-60=360-60 \\ 4x=300 \\ (4)/(4)x=(300)/(4) \\ \\ x=75 \end{gathered}`

Use the value of x to find the measure of arc GJ:

`\text{mGJ}=x+58=75+58=133º`The measure of arc GJ is 133º