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# geometry

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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 $$\angle BXY$$.

tertre  Apr 21, 2018

#1
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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
+942
+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
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Thanks for the detailed explanation, Gavin!

tertre  Apr 21, 2018