The sum of the interior angles of a triangle is 180°.
Let's suppose that all 3 angles in the ratio are divisible by a value x.
So the three angles become 1x, 2x and 3x.
1x + 2x + 3x = 180°
6x = 180°
x = 30° [ By dividing both sides by 6 ]
Thus the three angles are: 1x = 30° ; 2x = 2*30 = 60° ; 3x = 3*x = 90°
Hence the smallest angle is 30°.
