Question

If three angles of a triangle are in the ratio 2:3:4, then the measure of the three angles are:

• A. ${20}^{\circ },{60}^{\circ },{100}^{\circ }$
• B. ${40}^{\circ },{60}^{\circ },{80}^{\circ }$
• C. ${40}^{\circ },{50}^{\circ },{90}^{\circ }$
• D. ${50}^{\circ },{60}^{\circ },{70}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ },{60}^{\circ },{80}^{\circ }$

Let the three angles of a triangle be 2x, 3x, 4x.
$\because$ Sum of the angles in a triangle = ${180}^{\circ }$
$\Rightarrow 2x+3x+4x={180}^{\circ }$
$\Rightarrow 9x={180}^{\circ }$
$\Rightarrow x={20}^{\circ }$
$\Rightarrow 2\left({20}^{\circ }\right)={40}^{\circ },3\left({20}^{\circ }\right)={60}^{\circ }and4\left({20}^{\circ }\right)={80}^{\circ }$.