In ∆abc the angle bisectors drawn from vertices a and b intersect at point d. find ∠adb if: m∠с = γ

  90° + (γ/2)

Step-by-step 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°)

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80