In triangle ABC ∠A = 25 °, BM is the bisector of angle B, ∠СМB = 70 °. Find the degree measure ∠C.

The angles of a triangle add up to 180 degrees.
The sum of adjacent angles is 180 degrees.
The angles CMB and AMB are adjacent, and the angle CMB = 70, which means the angle AMB = 180 – CMB = 180-70 = 110 degrees.
Consider triangle AMB. Knowing what the angles A and AMB are equal to, we can find the angle ABM: ABM = 180 – A – AMB = 180-25-110 = 45 degrees. Angle ABM is equal to half of angle B, since BM is a bisector. This means that the angle B is 45 * 2 = 90 degrees.
Knowing the angles A and B, we find the angle C: 180-25-90 = 65 degrees.