In a triangle, all three angles must have a sum of 180 degrees.

In order to solve this problem, we will write each angle as an algebraic expression. Since angle 2 and angle 3 are in relation to angle 1, we can say that:

`/_1=x` Since the 2nd angle is 3 times as large as first, we can say:

`/_2 = 3x` Since the 3rd angles is 30 more than the 1st, we can say:

`/_3 = x + 30` Since all 3 together must have sum of 180, we can say:

`(x) + (3x) + (x + 30) = 180` Solve for x

`5x +30 = 180` Subtract 30.

`5x = 150` Divide by 5.

`x = 30`

So the 1st angle is 30 degrees, the second angle is 90 degrees and the 3rd angle is 60 degrees.

**Smallest = 1st angle of 30 degrees**

**Middle Angle = 3rd angle of 60 degrees**

**Largest angle = 2nd angle of 90 degrees**

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