Question

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

Answer 1

In $△ABC,2\angle A=3\angle B=6\angle C$

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

$⟹\angle B=\frac{6}{3}\angle C=2\angle C$

As we know that

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

$⟹3\angle C+2\angle C+\angle C={180}^{\circ }$

$⟹6\angle C={180}^{\circ }$

$⟹\angle C={30}^{\circ }$

$⟹\angle A=3\angle C=3\times {30}^{\circ }={90}^{\circ }$

$⟹\angle B=2\angle C=2\times {30}^{\circ }={60}^{\circ }$