Answer:
Step-by-step explanation:
Arc CD is 86°.
Angle EPF is 116°.
Arc CG is 148°.
[tex]\angle EPF + \angle FPD = 180\°\\116\°+ \angle FPD = 180\°\\\angle FPD = 180\° - 116\°\\\angle FPD = 64\°[/tex] By supplementary angles, and basic algebra.
[tex]\angle FPD = \frac{1}{2}(m(CG)-m(DF) )[/tex]
Solving for arc DF
[tex]64\° =\frac{1}{2}(148\° - m(DF)) \\2(64-74)=m(DF)\\m(DF)=20\°[/tex], by the theorem of the external angle formed by two secants.
Now, we know that the total arc lenght of a circle is 360°, so
[tex]m(CD)+m(CG)+m(FG)+m(DF)=360\°\\86+148+m(FG)+20=360\\m(FG)=360-254\\m(FG)=106\°[/tex]
Therefore, the measure of the arc FG is 106°.
Answer:
106 degrees is correct.
Step-by-step explanation:
I just tested it in Plato and got a 100%
