In a Find the three angles.

Given that,

∠ C = 3∠ B = 2(∠ A + ∠ B) 3∠ B = 2(∠ A + ∠ B)

3∠ B = 2∠ A + 2∠ B

∠ B = 2∠ A

2 ∠ A - ∠ B = 0 … (i)

We know that the sum of the measures of all angles of a triangle is 180°. Therefore,

∠ A + ∠ B + ∠ C = 180°

∠ A + ∠ B + 3 ∠ B = 180°

∠ A + 4 ∠ B = 180° … (ii)

Multiplying equation (i) by 4, we obtain 8 ∠ A - 4 ∠ B = 0 … (iii)

Adding equations (ii) and (iii), we obtain 9 ∠ A = 180°

∠ A = 20°

From equation (ii), we obtain 20° + 4 ∠ B = 180°

4 ∠ B = 160°

∠ B = 40°

∠ C = 3 ∠ B

= 3 x 40° = 120°

Therefore, ∠ A, ∠ B, ∠ C are 20°, 40°, and 120° respectively.