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.
