Question

Circle H is inscribed with quadrilateral D E F G. Angle E is 123 degrees. The measure of arc D E is 73 degrees.
What is the measure of arc EF in circle H?

41°
50°
114°
173°

Answer 1

An inscribed angle equals half its intercepted arc. Angle E = 123° intercepts arc DF, so arc DF = 2·123° = 246°. Arc DF is the rest of the circle besides arcs DE and EF, so 246° = 360° − (DE + EF). Thus DE + EF = 114°, and EF = 114° − 73° = 41°.