Given:
- The measure of the arc FG:
[tex]mFG=140\text{\degree}[/tex]
- The measure of the inscribed angle EGF:
[tex]m\angle EGF=46°[/tex]
You need to remember that, by definition:
• A circle has 360 degrees.
,
• Where there is an inscribed circle, the measure of the intercepted arc is twice the measure of the inscribed circle.
Therefore, you can set up this equation to find the measure of the arc EG:
[tex]mEG=360°-2(46°)-140°[/tex]
Evaluating, you get:
[tex]mEG=360°-92°-140°[/tex][tex]mEG=128°[/tex]
Hence, the answer is:
[tex]mEG=128°[/tex]
