Question

In ∆ABC, if ∠B is 3 times ∠A and ∠C is 2 times ∠A, then find the angle

Answer 1

In ABC, Let ∠A = x,

then ∠B = 3 times ∠A = 3x

∠C = 2 times ∠A = 2x

By angle sum property of a triangle,

Sum of three angles of ∆ABC = 180°

∠A + ∠B + ∠C = 180°

x + 3x + 2x = 180°

x(1 + 3 + 2) = 180°

6x = 180°

x = `(180^circ)/6` = 30°

∠A = x = 30°

∠B = 3x = 3 × 30° = 90°

∠C = 2x = 2 × 30° = 60°

∴ ∠A = 30°

∠B = 90°

∠C = 60°