Question

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

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

Answer 1

The correct option is D ${40}^o$

Given angles of triangles are in ratio 2:3:4.

Let the angles of triangle be x,y,z.

$x:y:z=2:3:4$

$\Rightarrow x=2k,y=3k,z=4k$

$x+y+z={180}^{\circ }$ ($\because$sum of angles of a triangle is ${180}^{\circ }$)

$\Rightarrow x+y+z=2k+3k+4k={180}^{\circ }$

$\Rightarrow 9k={180}^{\circ }$

$\Rightarrow k=\frac{{180}^{\circ }}{9}={20}^{\circ }$

$x=2k={40}^{\circ }$

$y=3k={60}^{\circ }$

$z=4k={80}^{\circ }$

Difference between highest and smallest is ${80}^{\circ }$- ${40}^{\circ }$$={40}^{\circ }$..