In an isosceles triangle ABC, with base AC = 42 cm, outside angle at apex C = 120 °. Find the lateral sides of angle ABC.

1. We calculate the value of the inner angle of the triangle at the vertex C, adjacent to the outer angle at the same vertex:

ACB angle = 180 ° – 120 ° = 60 °.

2. Angle A is equal to angle B as the angles at the base of an isosceles triangle.

Angle A = angle B = 60 °.

3. We calculate the value of the angle B:

Angle B = 180 ° – 60 ° – 60 ° = 60 °.

4. All three angles of the triangle are equal. Therefore, triangle ABC is equilateral:

AB = BC = AC = 42 cm.

Answer: the sides of the triangle AB = BC = 42 cm.