The ratio of the measures ∠A and ∠B of a triangle ABC is 3 : 2. The ratio of the measures of ∠B and ∠C is 4 : 5. Find the measure of largest angle of the triangle ABC.

Question: The ratio of the measures ∠A and ∠B of a triangle ABC is 3 : 2. The ratio of the measures of ∠B and ∠C is 4 : 5. Find the measure of largest angle of the triangle ABC.

Solution:
∠ A : ∠ B = 3 : 2.
∠ B : ∠ C = 4 : 5.
∴ ∠ A : ∠ B : ∠ C = 6 : 4 : 5.
Let actual values are 6x, 4x and 5x.

So
6x + 4x + 5x = 180°
⇒ 15x = 180°
∴ x = 12°

So largest angle is 6(12°) = 72°