Let the largest angle in a triangle be x .
Then :-
The smallest angle :-
[tex] \frac{1}{3} x[/tex]
The third angle :-
[tex] \frac{2}{3} x[/tex]
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 :-
[tex]x + \frac{1}{3} x + \frac{2}{3} x = 180[/tex]
[tex]x + \frac{3}{3} x = 180[/tex]
[tex]x + \frac{1}{1} x = 180[/tex]
[tex]x + 1x = 180[/tex]
[tex]x + x = 180[/tex]
[tex]2x = 180[/tex]
[tex]x = \frac{180}{2} [/tex]
[tex]x = 90[/tex]
Which means :-
Measure of the largest angle = 90°
Measure of the smallest angle :-
[tex] \frac{1}{3} \times 90[/tex]
[tex] = 30°[/tex]
Measure of the third angle :-
[tex] \frac{2}{3} \times 90[/tex]
[tex] = 60°[/tex]
Therefore :-
The measure of the largest angle = 90°
The measure of the smallest angle = 30°
The measure of the third angle = 60°
