Question

If the angles of a triangle are in the ratio 2 : 3 : 4, determine all the angles of the triangle.

Answer 1

Let the angles of the triangle be $2x^{\circ },3x^{\circ }and4x^{\circ }$ ^.Then,

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

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

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

Therefore,

$2x^{\circ }=2\times {20}^{\circ }={40}^{\circ }$​

$3x^{\circ }=3\times {20}^{\circ }={60}^{\circ }$​

$4x^{\circ }=4\times {20}^{\circ }={80}^{\circ }$​

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