If angle def measures 70, what is the measure of arc dgf?

A circle measures 360°.

Since ∠DEF is equal to 70°, the rest of the circle will have a measure of 360 - 70 = 290°.

Central Angle and Arc relationship:
It states that the measure of the central angle and the arc that it intercepts are equal in measure.

Since ∠DEC is a central angle, its intercepted arc DF is also equal to 70°.

With this given facts, arc DGF is equal to 290°.

We can only solve for the degrees because radius is not given. Had it been given, the fraction 290°/360° will be multiplied to the circumference of the circle to get the length of the arc DGF.