Question

The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle . Find the measures of three angles

Answer 1

Let the smallest angle be $x$

Given that one angle is twice the smallest angle. Therefore, the angle measure is $2x$

Given that other angle is thrice the smallest angle. Therefore, the angle measure is $3x$

We know that sum of the angles in a triangle is ${180}^0$

Therefore, $x+2x+3x=180$

$⟹6x=180$

$⟹x={30}^0$

Therefore, the smallest angle measure is ${30}^0$ and

the other angle measures are ${60}^0,{90}^0$