# In a ABC, ∠C = 3 ∠B = 2(∠ A + ∠ B). Find the measure of each one of ∠A, ∠B and ∠C.

We know that the sum of angles of a triangle is 180°

i.e. ∠A + ∠B + ∠C = 180°

The given relation is ∠C = 3 ∠B = 2(∠A + ∠B) … (1)

3 ∠B = 2(∠A + ∠B)

3 ∠B = 2 ∠A + 2 ∠B

2 ∠A = ∠B

A = ∠B/2

Substituting values in terms of B in equation (1),

∠B/2 + ∠B + 3 ∠B = 180°

∠B/2 + 4 ∠B = 180°

∠B(9/2) = 180°

∠B = 180 × 9/2

∠B = 40°

Substituting B value in (1),

∠C = 3 ∠B = 3(40) = 120°

And ∠A = ∠B/2 = 40/2 = 20°

The measures are ∠A = 20°, ∠B = 40°, ∠C = 120°.

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