Question

The largest angle of a triangle is twice the sum of the other two. The smallest is one-fifth of the largest. Determine all the angles in degrees.

• A. ${120}^o,{36}^o,{24}^o$
• B. ${15}^o,{85}^o,{80}^0$
• C. ${85}^o,{15}^o,{80}^0$
• D. ${20}^o,{136}^o,{24}^0$

Answer 1

The correct option is A ${120}^o,{36}^o,{24}^o$

Let $\angle A$ is the largest and $\angle C$ is the smallest angle.

According to question:

$\angle A=2(\angle B+\angle C)$ and $\angle C=\frac{1}{5}\angle A$

$\therefore \angle B+\angle C=\frac{1}{2}\angle A$ ....(i) and $\angle C=\frac{1}{5}\angle A$ ...(ii)

since,

$\angle A+\angle B+\angle C={180}^o$ ...(iii)

$\therefore \angle A+\frac{1}{2}\angle A={180}^o$ (from (i))

$\therefore \frac{1}{2}\left(3\angle A\right)={180}^o$

$\therefore 3\angle A={360}^o\Rightarrow \angle A={120}^o$

So,

$\angle C=\frac{1}{5}\left({120}^o\right)={24}^o$ (using (ii))

On substituting the value of $\angle A$ and $\angle C$ in (iii). we get,

${120}^o+\angle B+{24}^o={180}^o$

$\therefore \angle B={36}^o$

$\therefore \angle A={120}^o,\angle B={36}^o,\angle C={24}^o$