Question

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

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

Answer 1

The correct option is D

${40}^{\circ }$

Given,
Ratio of angles of triangles $2:3:4$

Let the common factor(HCF) be $x^{\circ }.$

Angles of the triangle will be $2x,3x,4x$.

Now, sum of the three angles of a triangle is ${180}^{\circ }$.

$\therefore$ $2x+3x+4x=1809x=180x=\frac{180}{9}=\frac{20\times 9}{9}x={20}^{\circ }$

The angles are
$2\times 20={40}^{\circ }$
$3\times 20={60}^{\circ }$
$4\times 20={80}^{\circ }$

The difference between the greatest and smallest angle $={80}^{\circ }-{40}^{\circ }={40}^{\circ }$