Question

The measures of angles of a triangle are in the ratio $2:3:4$. Find the angles.

Answer 1

Given:

The ratio of three angles $=2:3:4$

Let the angles of the triangle be $2x,3x$ and $4x$

We know that, the sum of the angles of a triangle $={180}^{\circ }$

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

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

$\Rightarrow x=\frac{{180}^{\circ }}{9}$

$\Rightarrow x={20}^{\circ }$

Therefore, the angles are $2\times {20}^{\circ },3\times {20}^{\circ }$ and $4\times {20}^{\circ }$

Thus the angles of triangle are ${40}^{\circ },{60}^{\circ }$ and ${80}^{\circ }$.