Question

If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY? A) 120° B) 130° C) 140° D) 150°

Answer 1

The picture in the attached figure

we have
arc XV = 68°∠YUV = 36°
 we know that
The measure of the external angle is the semidifference of the arcs that it covers.
therefore
∠YUV =[arc VY-arc XV]/2

arc VY=[2*∠YUV]+arc XV----------> [2*36]+68---------> 140°

the answer is
the measure of arc VY is 140°