In triangle ABC, angle A = 70 degrees, angle C = 55 degrees. prove that triangle ABC is isosceles, and indicate its base

In triangle ABC, angle A = 70 degrees, angle C = 55 degrees. prove that triangle ABC is isosceles, and indicate its base. The segment ВM is the height of this triangle. find the angles by which it divides the angle ABC.

The angles of a triangle add up to 180 °
It turns out:
70 ° + 55 ° + x = 180 °
x = 55 °
Therefore AC = AB, and BC-base
Consider triangle BMA. The sum of angles is also 180 °
Angle BMA = 90 °, because this is the height
BAM angle = 70 °
Hence the angle ABM = 180 ° -90 ° -70 ° = 20 °
The whole angle B is 55 °, so the angle MBC = 55 ° -20 ° = 35 °