Find ∠DEF if the arc degrees DE and EF are 150 ° and 68 °, respectively.

DEF angle – inscribed. The degree measure of the inscribed angle is equal to half the degree measure of the arc on which it rests. DEF is supported by DF. Find the degree measure of the arc DF:
arc DE + arc EF + arc DF = 360 degrees (since all arcs together form a circle);
150 + 68 + arc DF = 360;
arc DF = 360 – 218;
arc DF = 142 degrees.
The DEF angle is:
angle DEF = arc DF / 2;
angle DEF = 142/2 = 71 (degree).
Answer: angle DEF = 71 degrees.