The outer angle at the base of an isosceles triangle refers to the adjacent angle as 2 to 3

The outer angle at the base of an isosceles triangle refers to the adjacent angle as 2 to 3, define the angles of the triangle.

Since the triangle ABC is isosceles, then let AB = CB, and the outer angle at the vertex B is equal to 2 * X0, the angle CBK = 2 * X0, then, by condition, the inner angle ABC = 3 * X0.

Since the angles СВK and ABC are adjacent, then (* X + 3 * X) = 180.

5 * X = 180.

X = 180/5 = 360.

Then the angle ABC = 3 * 36 = 108.

The angle BAC = BCA, since the triangle is isosceles, then the angle BAC = BCA = (180 – 108) / 2 = 36.

Answer: The angles of the triangle ABC are 36, 36, 108.