Answer:
m UV = 118°
Step-by-step explanation:
The measure of the inscribed angle VUW is half the measure of its intercepted arc VW , then
VW = 2 × ∠ VUW = 2 × 31° = 62°
UW is the diameter of the circle, then m WU = 180°
The sum of the arcs on a circle is 360° , that is
UV + VW + WU = 360°
UV + 62° + 180° = 360°
UV + 242° = 360° ( subtract 242° from both sides )
UV = 118°
