In triangle ABC there is CM-median, angle ACB = 90, angle B = 55. Find the ACM angle.

1. According to the problem statement, the СM median is drawn from the vertex of the right angle. Therefore, according to its properties, it is equal to half of the hypotenuse AB.

2. Based on the foregoing, we come to the conclusion that the AFM triangle is isosceles, since AM = BM = CM. Therefore, AM = CM.

3. In such a triangle, the angles at its base are also equal. ∠CAM = ∠АСМ.

4. We calculate the value of ∠A, taking into account that the sum of all the inner angles of the triangle is 180 °:

180 ° – 90 ° – 55 ° = 35 °.

5. The sought ∠АСМ = ∠САМ = 35 °.

Answer: ∠АСМ = 35 °.