The bisector CD is drawn in an isosceles triangle ABC with a base AC. Find the angles of triangle ABC if ADC = 60 Degrees.

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

Let the angle BAC = BCA = 2 * X0.

Since CK is the bisector of the angle BCA, then the angle BCD = ACD = BCA / 2 = X0.

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

Then in the triangle ACD, (DAC + ACD + DKS) = 180.

(2 * X + X + 60 = 180.

3 * X = 120.

X = 120/3 = 40.

Angle BAC = BCA = 2 * 40 = 80, then angle ABC = (180 – 80 – 80) = 20.

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