Answer:
74°
Step-by-step explanation:
There are a couple of different angle relations that can be used to solve this problem. The measure of an inscribed angle is half the measure of the arc it subtends. The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. The measure of an exterior angle at the intersection of secants is half the difference of the arcs the secants subtend.
__
Using the secant relation, we find ...
∠Y = 1/2(RS -VX)
2×∠Y +VX = RS
2(28°) +18° = 74° = arc RS
__
Using the relations involving interior and exterior angles of a triangle, we have ...
∠S = 1/2(VX) = 1/2(18°) = 9°
∠RVS = ∠S +∠Y = 9° +28° = 37°
arc RS = 2×∠RVS = 2(37°) = 74°
