Question

In a triangle ABC, $\angle C=3\angle B=2(\angle A+\angle B)$. Find three angles in degrees

• A. ${20}^o,{50}^o,{120}^o$
• B. ${30}^o,{40}^o,{120}^o$
• C. ${20}^o,{40}^o,{120}^o$
• D. None of these

Answer 1

The correct option is C ${20}^o,{40}^o,{120}^o$

$\therefore \angle C=3\angle B=2(\angle A+\angle B)$
$\angle A+\angle B=\frac{\angle C}{2}$
We have,
$\angle A+\angle B+\angle C={180}^o$ (Sum of angles of a triangle is ${180}^o$)
$\frac{\angle C}{2}+\angle C={180}^o$
$3\angle C=2\times {180}^o$
$\angle C=\frac{2\times {180}^o}{3}={120}^o$
$3\angle B=\angle C$
$\angle B=\frac{\angle C}{3}$
$=\frac{{120}^o}{3}={40}^o$
$\therefore \angle A={180}^o-({120}^o+{40}^o)$$={180}^o-{160}^o={20}^o$