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 :-

$\frac{1}{3} x$

The third angle :-

$\frac{2}{3} x$

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 :-

$x + \frac{1}{3} x + \frac{2}{3} x = 180$

$x + \frac{3}{3} x = 180$

$x + \frac{1}{1} x = 180$

$x + 1x = 180$

$x + x = 180$

$2x = 180$

$x = \frac{180}{2}$

$x = 90$

Which means :-

Measure of the largest angle = 90°

Measure of the smallest angle :-

$\frac{1}{3} \times 90$

$= 30°$

Measure of the third angle :-

$\frac{2}{3} \times 90$

$= 60°$

Therefore :-

The measure of the largest angle = 90°

The measure of the smallest angle = 30°

The measure of the third angle = 60°