Question

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

Answer 1

Answer:

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♥

Answer 2

Answer :-

Let all angles be x

Then,

• ∠A = x/2

• ∠B = x/3

• ∠C = x/6

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

$= > \frac{6x + 4x + 2x}{12} = 180$

$= > \frac{12x}{12} = 180$

$= > x = 180$

__________________________

$∠a = \frac{x}{2} = \frac{180}{2} = 90$

$∠b = \frac{x}{3} = \frac{180}{3} = 60$

$∠c = \frac{x}{6} = \frac{180}{6} = 30$