The bisectors of angles A and B of triangle ABC meet at point M. Find the angle AMB, if angle A = 58 °, angle B = 96 °.

The bisector divides the angle into two equal angles, which means that in triangle ABM, angle A will be equal to half of angle A from triangle ABC, and angle B in triangle ABM will be equal to half of angle B from triangle ABC.

A = 58/2 = 29

B = 96/2 = 48

The angles of any triangle add up to 180 degrees. Knowing the magnitude of the angles A and B, we find the magnitude of the angle M in the triangle ABM.

180 – 29 – 48 = 103

Answer: in the triangle ABM, the angle M is 103 degrees