In the question it is already given that arc DEF is 266 degrees.From this information, we can say that
Arc DF = 360 - 266 degrees
= 94 degrees
We also know that
Inscribed angle = 1/2 of its arc
Then
Angle DEF = 1/2 * 94
= 47 degrees
From the above deduction, we can conclude that the measure of angle DEF is 47 degrees.
