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 °.
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