Question

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

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

Answer 1

The correct option is D ${40}^{\circ }$

Let the angles of the triangle be $2x,3x,4x$.
Now, sum of interior angles of a triangle is ${180}^{\circ }$.
$\Rightarrow 2x+3x+4x={180}^{\circ }$
$\Rightarrow 9x={180}^{\circ }$
$\Rightarrow x={20}^{\circ }$
The angles are ${40}^{\circ },{60}^{\circ },{80}^{\circ }$.
The difference between the largest and smallest angle is ${80}^{\circ }-{40}^{\circ }={40}^{\circ }$