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

[JayJay06]

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]

 

[soroban]

Re: please help

Hello, JayJay06!

It's quite straight-forward . . .

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

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

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

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

 

[JayJay06]

Thank you for the help.