Thread: Angle in a circle.

Segments RU, SV and TW are diameters of the circle.

Measure of angle RSO is 50 degrees.

If Segment TW bisects angle ROV, what is the measure of angle SOT?

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.

Yes, the un-drawn angle.

50 is correct.

Thanks for the help.