Question

In a triangle $ABC$ if $2\angle A=3\angle B=6\angle C$, then find $A,B,C$.

Answer 1

Let all the angles be $x$.

$\angle A=\frac{x}{2},\angle B=\frac{x}{3},\angle C=\frac{x}{6}$

So, $\frac{x}{2}+\frac{x}{3}+\frac{x}{6}=180°$ [sum of all the angles of triangle is $180°$]

$\frac{6x+4x+2x}{12}=180°$

$\frac{12x}{12}=180°$

$x=180°$

$\angle A=\frac{x}{2}=\frac{180°}{2}=90°$

$\angle B=\frac{x}{2}=\frac{180°}{3}=60°$

$\angle C=\frac{x}{6}=\frac{180°}{6}=30°$