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What is the size of angle ABE?

  1. Sep 3, 2005 #1
    hi everyone, there si this problem that i can't figure out and i was looking for some help

    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
  2. jcsd
  3. Sep 3, 2005 #2
    just draw and identify isosceles triangles.
    You will get 40 degrees
  4. Sep 7, 2005 #3
    i did what you said, but angle ABE was 70*
  5. Sep 7, 2005 #4
    ABE=40 degress.
    I think I have already posted it
  6. Sep 10, 2005 #5
    The solution:
    The symbol of degree is omitted.

    AD=BC (given)
    BE=DC (given)
    angleACD=180-angleBAC-angleADC (angle sum of triangle)
    Because angleACD=angleBAC
    Therefore DA=DC (sides opp. eq. angle)
    angleCDB=angleACD+angleCAD (ext. angle of triangle)
    angleCBD=angleCDB (base angles, isos. triangle)
    angleDCB=180-angleCBD-angleCDB (angle sum of triangle)
    angleCEB=angleECB (base angles, isos. triangle)
    angleABE+angleBAC=angleCEB (ext. angle of triangle)
    Last edited: Sep 10, 2005
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