Question

A triangle is such that the largest angle is three times the smallest angle. Find the measure of each angle

Answer 1

Let x represent the smallest angle. Then the largest is 3x, and the remaining angle is 180-4x. The problem statement tells us
.. 3x > 180 -4x > x
Adding 4x gives us
.. 7x > 180 > 5x
or
.. 36 > x > 180/7 = 25 5/7

The angles, smallest to largest, are
.. x, 4(45 -x), 3x
where 25 5/7 < x < 36

The angles could be, for example, any of ...
.. 26°, 76°, 78°
.. 30°, 60°, 90°
.. 32°, 52°, 96°
.. 35°, 40°, 105°
and an infinite number of other possibilities.