please help: In the figure AE is perpendicular to DG and....

JayJay06

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In the figure AE is perpendicular to DG and points B, X, and F are collinear. If XC bisects angle BXD and m<EXF = 28, find m< BXC.



I have been trying to solve this problem for a while now and no luck. May someone please help me.

Thank you.[/url]
 
Re: please help

Hello, JayJay06!

It's quite straight-forward . . .


In the figure. \(\displaystyle AE\,\perp\.DG\). points B\displaystyle B, X\displaystyle X, and F\displaystyle F are collinear.
If XC\displaystyle XC bisects BXD\displaystyle \angle BXD and \(\displaystyle m\angle EXF \,=\.28^o\), find mBXC\displaystyle m\angle BXC

We are told that: EXF=28o\displaystyle \,\angle EXF\,=\,28^o
Hence: AXB=28o  \displaystyle \,\angle AXB\,=\,28^o\; (vertical angles)

We are told that: AXD=90o\displaystyle \,\angle AXD\,=\,90^o
Then: BXD  =  AXDAXB  =  90o28o  =  62o\displaystyle \,\angle BXD\;=\;\angle AXD\,-\,\angle AXB\;=\;90^o\,-\,28^o\;=\;62^o

Since XC\displaystyle XC bisects BXD,BXC=31o\displaystyle \angle BXD,\:\angle BXC\:=\:31^o

 
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