Question

In ∆ABC the angle bisectors drawn from vertices A and B intersect at the point D. Find m∠ADB if
m∠A = α, m∠B = β

Answer 1

Answer: ∠ABD =  $\bold{\frac{1}{2}}$∠C

Step-by-step explanation:

$\angle A + \angle B + \angle C = 180^o\\\\\dfrac{1}{2}\angle A+\dfrac{1}{2}\angle B+\angle D=180^o\\\\\\\text{Solve the system by multiplying the second equation by -2}\\\angle A + \angle B + \angle C = 180^o\\\underline{-\angle A - \angle B - 2\angle D = -180^o}\\.\qquad \qquad \quad \angle C-2\angle D=0\\.\qquad \qquad \qquad \qquad \angle C=2\angle D\\.\qquad \qquad \qquad \quad \dfrac{1}{2}\angle C=\quad \angle D$