Question

In a ∆ABC, if $2\angle A=3\angle B=6\angle C$, calculate $\angle A,\angle B$ and $\angle C$.

Answer 1

Suppose: $2\angle A=3\angle B=6\angle C=x^{\circ }$
Then,$\angle A=(\frac{x}{2}{)}^{\circ }$ $\angle B=(\frac{x}{3}{)}^{\circ }$and $\angle C=(\frac{x}{6}{)}^{\circ }$
Sum of the angles of any triangle is 180°.
∠A +∠B +∠C = 180°
$\Rightarrow \frac{x}{2}+\frac{x}{3}+\frac{x}{6}=180$
$\Rightarrow \frac{3x+2x+x}{6}=180$
$\Rightarrow \frac{6x}{6}=180$
$\therefore x=180$
∴ ∠A=$\left(\frac{180}{2}\right)°$=90°
∠B =$\left(\frac{180}{3}\right)°=60°$ and $\angle C=\left(\frac{180}{6}\right)°=30°$