Triangle RSO is isosceles, so you can find its angles. Angle ROS = angle UOV. Then 360 - 2 * angle ROS = 2 * angle SOU = 2 * angle ROV, from where you an find SOU. Finally, OT bisects SOU.
Just to make sure, when you say "angle RSO" do you mean the measure of the un-drawn angle, or the measure of the angle of the arc? I'll assume the former in my response.
Given that all of these are diameters, all of the half-lines are radii of equal length and triangle RSO is isosceles. Thus angle ORS is also 50 and thus angle ROS is 80. Now the measure of angle ROV + measure of angle ROS completes a line and is thus equal to 180. But mROS = 80, thus mROV = 100 thus half of it is 50 which is mWOV which is vertical to SOT and thus mSOT is 50.