Question

The largest angle of a triangle is twice the sum of the other two and the smallest one is one fourth of the largest, the angles are

• A. ${120}^0,{40}^0,{20}^0$
• B. ${120}^0,{30}^0,{30}^0$
• C. ${90}^0,{45}^0,{45}^0$
• D. ${90}^0,{60}^0,{30}^0$

Answer 1

The correct option is B ${120}^0,{30}^0,{30}^0$

Let $a$ be largest angle and $c$ be smallest angle

$a=2(b+c)$ ....(1)
Also ,$c=\frac{1}{4}a\Rightarrow \frac{1}{2}(b+c)=c\Rightarrow b=c$ .....(2)
also, $a+b+c={180}^0$ ...(3)

$\therefore$ Solving (1), (2) and (3), we get, $a={120}^0,b={30}^0$and $c={30}^0$