Here the following side represent as 90°-45°-45° right angled triangle

=(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) etc

So the smallest angle = 45°

Next method,

Let the x= smallest angle,

we can also re write as: 3x + 4x + 5x = 180
or 12x = 180
or x= 15

Therefore the smallest angle = 3x = 3*15 = 45°
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A 45-45-90 triangle would have a ratio of x : x : \sqrt{2} ... your logic for first explanation is wrong but you came to a right conclusion by luck. Triangle can't be right-angled because then a 45 degree angle + 90 degrees means your third angle is also 45. 45:45:90 cannot have a 3:4:5 ratio because 3:4:5 is not x : x : \sqrt{2}

Your second method is correct nonetheless.