Question

In a triangle $ABC,$ of $2\angle A=3\angle B=6\angle C$ , then the measurement of $\angle B$ is?

Answer 1

Given: $2\angle A=3\angle B=6\angle C$

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

$\angle C=\frac{2}{6}\angle A=\frac{1}{3}\angle A$

We know that the Sum of all angles of a triangle is ${180}^{\circ }$

$\angle A+\angle B+\angle C={180}^{\circ }$

$\Rightarrow \angle A+\frac{2}{3}\angle A+\frac{1}{3}\angle A={180}^{\circ }$

$\Rightarrow 2\angle A={180}^{\circ }$

$\Rightarrow \angle A={90}^{\circ }$
We know $\angle B=\frac{2}{3}\angle A$
$\angle B=\frac{2}{3}\times {90}^{\circ }={60}^{\circ }$