Question

If the angles of a triangle are in the ratio $2:3:4,$ then the difference between the greatest and smallest angles is

• A. ${10}^{\circ }$
• B. ${20}^{\circ }$
• C. ${30}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

Answer: (D)

${40}^{\circ }$

Let the angles be in ratio $2x,3x,4x$.

Therefore, $2x+3x+4x=$ ${180}^{\circ }$
$9x=$ ${180}^{\circ }$
$x=$ ${20}^{\circ }$
Difference between the greatest and smallest angles is
$=4x-2x=2x$

$=2$ $\times {20}^{\circ }$

$={40}^{\circ }$