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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-> 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):
< 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 = = .
