The bisector BM is drawn in the triangle ABC, the degree measure of the angle AMB is equal to 120

The bisector BM is drawn in the triangle ABC, the degree measure of the angle AMB is equal to 120, the angle B is equal to 80. Find the angles of the triangle CBM.

Consider the triangle ABM, two angles are known in it:
∠ АМВ = 120 ° (by condition);
∠ ABM = ∠ B / 2 = 40 ° (BM – bisector).
Find the angle A (the sum of the angles of the triangle is 180 °)
∠ А = 180 ° – (40 ° + 120 °) = 20 °.
Two angles of the triangle ABC are known, we find the third angle, the angle C.
∠ С = 180 ° – (∠ А + ∠ В) = 180 ° – 100 ° = 80 °.
In the CBM triangle, the following are known:
∠ С = 80 °;
∠ СBМ = ∠ В / 2 = 40 ° (BM – bisector).
We find the angle of the CMB:
∠ CMB = 180 ° – (80 ° + 40 °) = 60 °.
Or
∠ CMB – adjacent to the angle AMB and is equal to:
∠ CMB = 180 ° – ∠ AMB = 180 ° – 120 ° = 60 °.
Answer: 40 °, 60 °, 80 ° are the angles of the CMB triangle.