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In the diagram, \(\angle U = 30^\circ\), arc \(XY\) is \(170^\circ\), and arc \(VW\) is \(110^\circ\). Find arc \(WY\), in degrees.

 Jan 25, 2021
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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°

 

 

cool cool cool

 Jan 25, 2021

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