Question

In a $△ABC$, if $2\angle A=3\angle B=6\angle C$, calculate the measures of $\angle B$ (in degrees).

Answer 1

$2\angle A=3\angle B$ .... (Given)

$\Rightarrow \angle A=\frac{3}{2}\angle B$

$3\angle B=6\angle C$ ..... (Given)

$\Rightarrow \angle C=\frac{1}{2}\angle B$

In a triangle, sum of all the angle will be $180°$.

$\therefore \angle A+\angle B+\angle C=180°$

$\Rightarrow \frac{3}{2}\angle B+\angle B+\frac{1}{2}\angle B=180°\{\because \angle A=\frac{3}{2}\angle B\&\angle C=\frac{1}{2}\angle B\}$

$\Rightarrow \frac{3\angle B+2\angle B+\angle B}{2}=180°$

$\Rightarrow \frac{6}{2}\angle B=180°$

$\Rightarrow \angle B=180°\times \frac{2}{6}$

$\Rightarrow \angle B=60°$