Question

In a triangle, the largest angle is ten times the smallest and the remaining angle is the square of the smallest. The largest angle of the triangle is

• A. ${80}^o$
• B. ${100}^o$
• C. ${120}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Let the smallest angle be x
Largest angle = 10 x
Remaining angle $=x^2$
$\therefore x^2+x+10x={180}^o$
$or{x}^2+11x-180=0$
$or(x+20)(x-9)=0$
$orx=9$ (Since the angle of a triangle cannot be negative)
Largest angle $=10x=10\times 9={90}^o$