Question

The smallest angle in a triangle is 1/3 as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.

Answer 1

Let the largest angle in a triangle be x .

Then :-

The smallest angle :-

`(1)/(3) x`

The third angle :-

`(2)/(3) x`

Let us find the measure of the three angles .

Sum of all angles in the interior of a triangle = 180°

An equation to find the value of each angle :-

`x + (1)/(3) x + (2)/(3) x = 180`

`x + (3)/(3) x = 180`

`x + (1)/(1) x = 180`

`x + 1x = 180`

`x + x = 180`

`2x = 180`

`x = (180)/(2)`

`x = 90`

Which means :-

Measure of the largest angle = 90°

Measure of the smallest angle :-

`(1)/(3) * 90`

`= 30°`

Measure of the third angle :-

`(2)/(3) * 90`

`= 60°`

Therefore :-

The measure of the largest angle = 90°

The measure of the smallest angle = 30°

The measure of the third angle = 60°