Answer:
The formula for the length of an arc of a circle is given by:
length of arc = (central angle/360) x 2πr
where r is the radius of the circle and the central angle is measured in degrees.
In this problem, we know the length of arc RV is 3π/2 units and the radius of circle M is 6 units. Therefore, we can solve for the central angle using the formula above:
3π/2 = (central angle/360) x 2π(6)
3π/2 = (central angle/180) x π x 6
3/2 = (central angle/180) x 6
central angle = (3/2) x (180/6) = 45 degrees
So the approximate measure of angle RMV is 45 degrees, which corresponds to option B.