Answer: [tex]149^{\circ}[/tex]
Step-by-step explanation:
From the given figure, the measure of central angle FDG is given by :-
[tex]\angle{EDG}=\angle{EDF}+\angle{FDG}\\\\=83^{\circ}+66^{\circ}\\\\=149^{\circ}[/tex]
We know that the measure of arc in degrees is equals the measure of the central angle that intercepts the arc.
Now,the measure of arc EFG is given by :-
[tex]Arc\ \text{EFG}=\text{Central angle EDG}=149^{\circ}[/tex]
