In isosceles triangle ABC with base AC, bisector CK is drawn. Find the angles of the triangle ABC

In isosceles triangle ABC with base AC, bisector CK is drawn. Find the angles of the triangle ABC if the angle AKC = 60 degrees.

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

Let the angle BAC = BCA = X0.

Since CK is the bisector of the angle BCA, then the angle BCA = ACK = BCA / 2 = X / 2.

The sum of the interior angles of a triangle is 180.

Then in the triangle ACK, (KAC + ACK + AKC) = 180.

(X + X / 2 + 60 = 180.

1.5 * X = 120.

X = 120 / 1.5 = 80.

Angle BAC = BCA = 80, then angle ABC = (180 – 80 – 80) = 20.

Answer: The angles of the triangle ABC are equal to 20, 80, 80.