Question

If the angles of a triangle are in the ratio $5:3:2$, then the triangle could be:

• A. obtuse
• B. acute
• C. right
• D. isosceles

Answer 1

The correct option is C right

Let the angles of the triangle be $5x,3x$ and $2x$.
Then, $5x+3x+2x={180}^{\circ }\Rightarrow 10x={180}^{\circ }$
$\Rightarrow x={18}^{\circ }$
$\therefore$ The angles are $5\times {18}^{\circ },3\times {18}^{\circ },2\times {18}^{\circ }$, i.e., ${90}^{\circ },{54}^{\circ }$ and ${36}^{\circ }$
Hence, the triangle is a right triangle.