The median BM is drawn in an isosceles triangle ABC with base AC. The BAC angle is known to be 57

The median BM is drawn in an isosceles triangle ABC with base AC. The BAC angle is known to be 57 °. Find the angles of triangle BCM.

Since the triangle ABC is isosceles, its median BM is also the height and the bisector.

Then the angle BMC = 90.

In an isosceles triangle, the angles at its base are equal, then the angle BCM = BAM = 57.

In a right-angled triangle, the sum of acute angles is 90, then the angle CBM = (90 – BCM) = (90 – 57) = 33.

Answer: The angles of the BCM triangle are 33, 57, 90.