Question

If the angles of a triangle are in the ratio 2 : 3 : 5, the triangle is ___

• A. acute angled
• B. obtuse angled
• C. Equilateral
• D. Right angled

Answer 1

The correct option is D

Right angled

Let the angles be $2x,3x\text{and}5x$
$2x+3x+5x={180}^{\circ }$... (Angle sum property)

$10x={180}^o$

$x={18}^{\circ }$

$\therefore$ The angles of the $\Delta$ are,
$2\left({18}^{\circ }\right)={36}^{\circ }$
$3\left({18}^{\circ }\right)={54}^{\circ }$
$5\left({18}^{\circ }\right)={90}^{\circ }$

Hence the triangle is a right angled triangle.