In an isosceles triangle ABC with a base AC, the angle C is 40 degrees, the angle B is 100 degrees.

In an isosceles triangle ABC with a base AC, the angle C is 40 degrees, the angle B is 100 degrees. The median BK is drawn. Find the angles of the triangle ABK.

Since the ABC triangle is isosceles, then its angles when warping are equal. Angle BAC = BCA = 40, then BAC = 40.

BK, by condition, is the median of the triangle ABC, and since it is isosceles, then BK is also the bisector of the angle ABC and the height of the triangle, then the angle ABK = СBK = ABC / 2 = 100/2 = 50, and the angle AKB = 90.

Answer: The angles of the ABK triangle are 40, 50, 90.