Question

If the angles of a triangle are in the ratio 1 : 2 : 3, determine three angles.

Answer 1

Ratio in three angles of a triangle = 1 : 2 : 3

Let first angle = x

Then second angle = 2x

and third angle = 3x

$\therefore$ x+2x + 3x = ${180}^{\circ }$ ( sum of angles of a triangle)

$\Rightarrow 6x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{6}={30}^{\circ }$

$\therefore$ First angle = $x={30}^{\circ }$

Second angle = $2x=2\times {30}^{\circ }={60}^{\circ }$

and third angle = $3x=3\times {30}^{\circ }={90}^{\circ }$

$\therefore$ Angles are ${30}^{\circ },{60}^{\circ },{90}^{\circ }$