What is the size of angle ABE?

[chickenguy]

hi everyone, there si this problem that i can't figure out and i was looking for some help
FIND THAT ANGLE!

In a triangle ABC, angleBAC=35*, D is a point on AB such that AD=BC and angle ADC=110*. E is a point on AC such that BE=DC. What is the size of angle ABE? :rofl:thx

 

[balakrishnan_v]

just draw and identify isosceles triangles.
You will get 40 degrees

 

[chickenguy]

i did what you said, but angle ABE was 70*

 

[balakrishnan_v]

ABE=40 degress.
I think I have already posted it

 

[ntcctnntcctn]

The solution:
The symbol of degree is omitted.

AD=BC (given)
BE=DC (given)
angleACD=180-angleBAC-angleADC (angle sum of triangle)
=180-35-110
=35
Because angleACD=angleBAC
Therefore DA=DC (sides opp. eq. angle)
angleCDB=angleACD+angleCAD (ext. angle of triangle)
=35+35
=70
DA=DC
DC=BC
angleCBD=angleCDB (base angles, isos. triangle)
=70
angleDCB=180-angleCBD-angleCDB (angle sum of triangle)
=180-70-70
=40
DC=BC
BE=BC
angleCEB=angleECB (base angles, isos. triangle)
=angleACD+angleDCB
=35+40
=75
angleABE+angleBAC=angleCEB (ext. angle of triangle)
angleABE+35=75
angleABE=40