Prove the exterior angle bisectors are equal

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Imagine a triangle with angles 132,36,12
I draw the exterior angles bisectors (132 and 12)
I want to prove that these bisectors are equal... Please take a look to the figure I want to prove that AM'=CM
I tried to use Stewart's theorem but I couldn't prove it..

Or let me ask my question Another way:
If we have a triangle that two exterior angle bisectors of that are equal, Can we say that our triangle is isosceles?
If we can not, please give me an example...