An isosceles triangle KLM with base KM has a bisector KN. Find the angles of a triangle KLM if the angle KNM is 66.

Since the KLM triangle is isosceles with the base of the KM, then the angle LMB = LMK.

Let the angle LMC = LMC = 2 * X0.

Since the segment KN is the bisector of the LKM angle, the LKN angle = MKN = LKM / 2 = 2 * X / 2 = X0.

The sum of the interior angles of the triangle is 180, then in the KMN triangle:

KMN + MKN + KNM = 180.

2 * X + X + 66 = 180.

3 * X = 114.

X = 114/3 = 38.

Then the angle LMB = LMC = 2 * 38 = 76.

KLM angle = 180 – 76 – 76 = 28.

Answer: The angles of triangle ABC are equal to 28, 76, 76.