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

The bisector of the angle at the base of an isosceles triangle is equal to the base of the triangle. define the corner opposite to the base.

Consider a triangle ADС, in which BP = AC by the condition, the angle of DAC is equal to half of the angle of BAC, since BP is the median.

Let’s designate the angle BAC through X, then the angle DAС = X / 2.

The DAС triangle is isosceles, therefore the angles at the base of the СD are equal to each other.

Since the triangle ABC is isosceles by the condition, then the angle BAC = angle BCA = X, then the angle ADС = AСD.

Then X + X + X / 2 = 180.

2 * X + 2 * X + X = 360.

5 * X = 360.

X = 360/5 = 72.

Answer: The angle at the base is 72.