Bisector AO is drawn in triangle ABC; angle C = 44; angle AOB = 74; find angle B.

We find the angle AOC – it is adjacent to the angle AOB:
∠ AOC = 180 ° – ∠ AOB = 180 ° – 74 ° = 106 °.
Two angles are known in the AOC triangle, we find the third angle of the AOC:
∠ OAC = 180 ° – (∠ AOC + ∠ OCA) = 180 ° – (106 ° + 44 °) = 180 ° – 150 ° = 30 °
∠ BAC = 2 * ∠ OAC = 2 * 30 ° = 60 ° (AO – bisector).
In triangle ABC we find angle B:
∠ B = 180 ° – (∠ A + ∠ C) = 180 ° – (60 ° + 44 °) = 180 ° – 104 ° = 76 °.
Answer: The degree measure of angle B is 76 °.