Question

In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if:

m∠A = α , m∠B = β

Answer 1

The measure angle ADB = 180 - (α/2+ β/2)

Explanation:

measure angle A is α degrees, this means that, the angle bisector divides the angle into two equal angles each of measure α/2 degrees

measure angle B is β degrees, this means that the angle bisector divides the angle into two equal angles each of measure β/2 degrees

In triangle ADB, we know that the sum of all measure of a triangle is 180 degrees and we have measure angle MAB = α/2 degrees and measure angle MBA = β/2 degrees

Therefore,

measure angle ADB = 180 - (α/2+ β/2)