In an isosceles triangle ABC with base AC, the bisectors AF and CK meet at point O.

In an isosceles triangle ABC with base AC, the bisectors AF and CK meet at point O. Find the degree measure of the angle AOC if the angle B is 20 degrees.

Since the triangle ABC is isosceles, the angles at its base AC are equal. Angle BAC = BCA.

The sum of the inner angles of the triangle is 180, then the angle BAC = BCA = (180 – ABC) / 2 = (180 – 20) / 2 = 160/2 = 80.

Since AF and CK are the bisectors of the angles, the angle OAC = OCA = BAC / 2 = 80/2 = 40.

Then the angle AOC = 180 – 40 – 40 = 100.

Answer: The AOC angle is 100.