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

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.