One corner of a triangle is 2 times less than the second, 3 times less than the third angle. What are the angles of a triangle?

Let a triangle ABC be given, in which the smaller angle BAC is x degrees, then the average angle ABC will be (2 ∙ x) degrees, and the largest angle ACB will be (3 ∙ x) degrees, since one angle of the triangle is half the second and three times less than the third corner. Knowing from geometry that the sum of the angles in a triangle is 180 °, we compose the equation:

x + 2 ∙ x + 3 ∙ x = 180;

6 ∙ x = 180;

x = 30 (degrees) – the value of the smaller angle BAC;

2 ∙ 30 = 60 (degrees) – the value of the average angle ABC;

3 ∙ 30 = 90 (degrees) – the value of the greater angle ACB.

Answer: 30 °, 60 °, 90 °.