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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.

 

 

 

 

 

ANSWER NOT 55
 

 Apr 10, 2020
edited by ilikepokemon2009  Apr 10, 2020
 #1
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-1

See https://web2.0calc.com/questions/plz-help-asap_33

 Apr 10, 2020
 #2
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The answer was wrong.

 Apr 10, 2020
 #3
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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

 

 

cool cool cool

 Apr 10, 2020

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