Answer:
234°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of the arc it intercepts. That is the same as saying the measure of the arc is twice the measure of the inscribed angle intercepting it.
An inscribed angle is generally defined by 3 points on the circle: two at the ends of the arc, and one at the vertex of the angle. As the vertex of the angle gets closer to one of the ends of the arc, the chord between the two points (vertex and arc end) becomes closer and closer to a tangent to the circle.
The relationship between the angle measure and the arc measure remains true, even when the angle is between a tangent (line t) and the chord to the other end of the arc (segment DF). That is, the intercepted arc is twice the angle measure:
Arc DEF = 2 × ∠D = 2 × 117° = 234°
