help geometry

Since there are 360^o in the circle and arc(XY) = 170^o and arc(VW) = 120^o,

there is a total of 170^o + 120^o = 290^o in these two angles (combined);

this means left over for arc(XV) and arc(WY) (combined).is 360^o - 290^o  =  70^o.

 

Let x = arc(WY)     --->      then arc(XV) = 70^o - x

 

Since angle(U) is an angle in the exterior of the circle:  [ x - (70^o - x) } / 2  =  30^o.

 

Solving,  x = 65^o.