+20 In the diagram, \(\angle U = 30^\circ\), arc XY is \(170^\circ\), and arc VW is \(110^\circ\). Find arc WY, in degrees.
ANSWER NOT 55
+128407 measure of angle U = (1/2)( arc WY - arc XV)
30 = (1/2) ( arc WY - arc XV) (1)
Note that angle VXW = (1/2)arc VW = 55
And angle XVY = (1/2) arc XY = 85
Call the intersection of chords VY and XW , E
So in triangle XVE, angle XEV =180 - angle VXW - angle XVY = 180 - 55 - 85 = 40
And by the intersecting chord theorem,
angle XEV = (1/2) ( arc WY + arc XV)
40 = (1/2) (arcWY + arc XV) (2)
Using (1) and (2) we have that
30 = (1/2)arc WY - (1/2)arc XV
40 = (1/2) arc WY + (1/2)arc XV add these
70 = arc WY
