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

Given:

The angles of a triangle are in the ratio $1:2:3$.

To do:

 We have to determine three angles.

Solution:

We know that,

Sum of the angles in a triangle is $180^o$.

Let the three angles of the triangle be $\angle A=x, \angle B=2x, \angle C=3x$

Therefore,

$\angle A + \angle B + \angle C = 180^o$

$x+2x+3x=180^o$

$6x=180^o$

$x=30^o$

This implies,

$2x=2(30^o)=60^o$

$3x=3(30^o)=90^o$

Hence, the three angles are $30^o, 60^o$ and $90^o$.