The bisector of an isosceles triangle is equal to the base of the triangle. Determine the angle opposite the base.

Let the angle at the base of the AC be equal to X0. Angle BAC = BCA = X0.

Since AM is the bisector of the angle BAC, then the angle MAC = BAC / 2 = X / 20.

By condition, the bisector AM is equal to the base of the AC, then the triangle AFM is isosceles, and therefore the angle AСM = AMC = X0.

The sum of the interior angles of the AСM triangle is 180, then:

X + X + X / 2 = 180.

5 * X / 2 = 180.

5 * X = 36.

X = 72.

Angle MAC = BAC = 72.

Then the angle ABC = (180 – 72 – 72) = 36.

Answer: The angle opposite to the base is 36.