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In the diagram below, line MN is a diameter of the circle. Find angle XYZ, in degrees.

Diagram: https://latex.artofproblemsolving.com/b/5/c/b5ca879e6891c11d8a31ce8210b4763a6e773423.png

tysm <3

 Mar 23, 2020
 #1
avatar+111330 
+2

Note that  

 

Angle M  = (1/2) its intercepted arc  =  (1/2)(80)   = 40°

 

Similarly, angle N = (1/2) 35  =  17.5°

 

Then in triangle MYN  angle MYN   =180 - 40 - 17.5  = 122.5°

 

But  angle XYZ  is a vertical  angle to angle MYN  so it also measures 122.5°

 

 

cool cool cool

 Mar 23, 2020
 #2
avatar+724 
+2

CPhill is (this time)smileycorrect.

Line WO bisects angle MOX and it's parallel to XY

Line VO bisects angle NOZ and it's parallel to YZ

∠WOV = ∠XYZ = 180° - ( 40° + 17.5° )

 

 Mar 23, 2020
edited by Dragan  Mar 23, 2020
edited by Dragan  Mar 23, 2020

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