In the diagram, \(\angle U = 30^\circ\), arc \(XY\) is \(170^\circ\), and arc \(VW\) is \(110^\circ\). Find arc \(WY\), in degrees.
+128475 Call the intersection of XW and VY, T
In triangle XTV
Angle VXT = (1/2) arc VW = 55°
Angle XVT = (1/2) arc XY = 85°
Then angle XTV = 180 - 55 - 85 = 40°
And by the interesecting chord theorem
Angle XTV = (1/2) (arc WY + arc VW) = 40 ⇒ arc WY + arc VW = 80 (1)
And Anhle XUV = (1/2) (arc WY - arc VW) = 30 ⇒ arc WY - arc VW = 60 (2)
Add (1) and (2)
2arc WY = 140
arc WY = 70°
