Question

In ∆ABC the angle bisectors drawn from vertices A and B intersect at point D. Find ∠ADB if: m∠С = γ

Answer 1

90° + (γ/2)

Explanation:

The angles in ΔADB have a sum of 180°, so ...

(A/2) +(B/2) + ∠ADB = 180°

and so do the angles of ΔABC:

A + B + γ = 180°

Dividing this second equation by 2 gives an expression for (A/2) +(B/2) that we can substitute into the first equation:

A/2 +B/2 +γ/2 = 90°

A/2 +B/2 = 90° -γ/2

Putting this in the first equation, we have ...

(90° -γ/2) + ∠ADB = 180°

∠ADB = 90° +γ/2 . . . . . . . . . . add (γ/2 -90°)