Triangle problem

[Matthew 37]

I am a teacher, practicing my student for competition then i got a sample question about a triangle. I try algebra approach but does not work, then i cant use similar triangle. i got confuse what approach should i use to teach my student. The question is find the value of angle X in the figure, AD=DC BC=AE and angle ACB = 75 degree.

 

[lev888]

I would start with drawing EC.

 

[Matthew 37]

I would start with drawing EC.

But it does not do any thing no theorem support to solve x.

 

[lev888]

But it does not do any thing no theorem support to solve x.

What theorem?
It does create a useful triangle EBC. I expressed its angles through x and set up the equation for sum of angles = 180.

 

[Dr.Peterson]

Do you see how long EC has to be?

 

[Matthew 37]

Do you see how long EC has to be?

no given sir.

 

[lev888]

no given sir.

You mentioned that you are a teacher. What exactly do you teach?

 

[Dr.Peterson]

no given sir.

What kind of triangle is AEC (knowing that the perpendicular bisector of AC passes through E)?

(You didn't say in words that DE is perpendicular to AC, but the picture indicates it.)

 

[Matthew 37]

Yes i see it now sir. thanks for the help...the x= 35 degree

 

[hoosie]