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Math Help - triangle

  1. #1
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    triangle

    http://img395.imageshack.us/img395/9...heangelfk4.png

    all the angles are given how do u find the angle that has a question mark beside it?
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  2. #2
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    Krizalid's Avatar
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    The answer is \measuredangle~\alpha=20^\circ

    Try it!

    It's a beautiful problem.

    Of course, don't even think use trig.
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  3. #3
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    how did u get that?
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  4. #4
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    Klicken sie Heir.

    Sorry, Krizalid I used trigonometry to solve it. I am not as good in Classical Geometry as you are.
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  5. #5
    Math Engineering Student
    Krizalid's Avatar
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    Here's a picture




    Take a point F such that \overline{CF}=\overline{CE}~\wedge~\measuredangle~  BCF=20^\circ

    You need to prove two facts:
    • \overline{AD}=\overline{BC}
    • D,\,E,\,F are collinear.
    Finally, you'll see that quadrilateral BCDF is cyclic, and the problem is done.

    Good luck!
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