Question

In a ∆ABC, if 2 ∠A = 3 ∠B = 6 ∠C then calculate  ∠A,  ∠B and  ∠C.​

Answer 1

Let $2 ∠A = 3 ∠B = 6 ∠C = x°$

Then,

$∠A = ( \frac{x}{2}° ) ;∠B = ( \frac{x}{3} °)and \: ∠C =( \frac{x}{6}° )$

$But , ∠A + ∠B + ∠C = 180°$

$.°. \frac{x}{2} + \frac{x}{3} + \frac{x}{6} = 180$

$\implies 3x + 2x + x = 1080$

$\implies 6x = 1080$

$\implies x = \frac {1080}{6} = 180$

$.°. ∠A = \frac { 180}{2}°= 90°$

$.°. ∠B = \frac { 180}{3}°= 60°$

$.°. ∠C = \frac { 180}{6}°= 30°$

Hence, ∠A = 90° , ∠B = 60° and ∠C = 30°

Hope it helps♥.