SOLUTION: In △ABC the angle bisectors drawn from vertices A and B intersect at point D. Find ∠ADB if: a. ∠A =α, ∠B=β b. ∠C= γ

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Question 1123946: In △ABC the angle bisectors drawn from vertices A and B intersect at point D. Find ∠ADB if:
a. ∠A =α, ∠B=β
b. ∠C= γ
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
    < ADB = 180° - (half of < A + half of < B)     (1)    (as the sum of interior angles of the triangle ABD)



From the other side

      < A + < B + < C = 180°  ====>  half of < A + half of < B = 90° - half < C.



Therefore, you can continue (1) in this way :


    < ADB = 180° - (half of < A + half of < B) = 180° - (90° - half < C) = 90° + half < C.



Or, in terms of  ,    and  


    < ADB =  = .

Solved.


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