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In the diagram below, \(\overline{AB}\parallel \overline{CD}\)  and \(\angle AXE\) is \(108^\circ\) less than 3 times \(\angle CYX\). Find \(\angle BXY\).

 

 Apr 21, 2018

Best Answer 

 #1
avatar+972 
+5

Hi tertre,

 

Since line AB is parallel to line CD, angle AXE is equal to CYX.

 

This means we can set angle AXE = angle CYX = x

 

Since AXE is 108º less than 3 times CYX, we have this:

 

\(x+108=3x\)

 

Solving for x, we get:

 

\(x=54\)

 

We know that AXE and CYX = 54º

 

Since AXE and BXY are congruent angles, we know that

 

\(BXY=54º\)

 

I hope this helps, 

 

Gavin

 Apr 21, 2018
 #1
avatar+972 
+5
Best Answer

Hi tertre,

 

Since line AB is parallel to line CD, angle AXE is equal to CYX.

 

This means we can set angle AXE = angle CYX = x

 

Since AXE is 108º less than 3 times CYX, we have this:

 

\(x+108=3x\)

 

Solving for x, we get:

 

\(x=54\)

 

We know that AXE and CYX = 54º

 

Since AXE and BXY are congruent angles, we know that

 

\(BXY=54º\)

 

I hope this helps, 

 

Gavin

GYanggg Apr 21, 2018
 #2
avatar+3994 
+2

Thanks for the detailed explanation, Gavin! smileysmiley

tertre  Apr 21, 2018

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