# 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.

BE=DC (given)
=180-35-110
=35
Because angleACD=angleBAC
Therefore DA=DC (sides opp. eq. angle)
=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

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