In an isosceles triangle ABC, the bisector AE was drawn so that the triangle AEB

In an isosceles triangle ABC, the bisector AE was drawn so that the triangle AEB is isosceles. Find the angle C of the original triangle (in degrees).

By condition, triangle AEB is isosceles, then the angle BAE = ABE.

Let the angle BAE = ABE = X0.

AE is the bisector of angle A, then the angle ABC = 2 * X0.

The ABC triangle is isosceles, then the angle BAC = BCA = 2 * X0.

The sum of the interior angles of the triangle is 180, then 2 * X + X + 2 * X = 180.

5 * X = 180.

X = 180/5 = 36.

Then the angle C = 2 * 36 = 72.

Answer: Angle c is 72.