In the diagram, angle u= 30 degrees. Arc XY is 170 degrees, and arc VW is 120 degrees. Find arc WY, in degrees.
Since there are 360o in the circle and arc(XY) = 170o and arc(VW) = 120o,
there is a total of 170o + 120o = 290o in these two angles (combined);
this means left over for arc(XV) and arc(WY) (combined).is 360o - 290o = 70o.
Let x = arc(WY) ---> then arc(XV) = 70o - x
Since angle(U) is an angle in the exterior of the circle: [ x - (70o - x) } / 2 = 30o.
Solving, x = 65o.