The bisector of the angle at the base of an isosceles triangle intersects the lateral side at an angle equal

The bisector of the angle at the base of an isosceles triangle intersects the lateral side at an angle equal to the angle at the base. Find the corner at the base.

Let the angles at the base of an isosceles triangle be <BAC = <BCA = x.

Then the triangle cut off by the bisector AN from the original triangle ABC will have angles:

<NAB = x / 2 – obtained by dividing the angle at the base by the bisector;

<NCA = x – second angle at the base of the original triangle;

x is the angle at which the bisector crosses the side BC;

The sum of the angles of triangle ANC is 180 °:

x / 2 + x + x = 180 °;

5x / 2 = 180 °;

5x = 360 °;

x = 72 °.

Answer: 72 °.