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

tertre
Apr 21, 2018

#1**+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

GYanggg
Apr 21, 2018

#1**+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