Question

Given that ∠ABC is bisected by BD→, m∠ABD = (-159 – 12x)°, and m∠DBC = (3x + 96)°, find x and m∠ABC.

Answer 1

When anything is bisected, the two halves are equal. This means
(-159 - 12x) = (3x + 96)
-255 = 15x . . . . . . . . . . . . . add 12x-96
-17 = x

Then either of the smaller angles is
(3(-17) + 96)° = 45°

angle ABC is twice this value, or 90°.