The measures of all of the interior angles of a triangle are in the extended ratio 1 : 2 : 3. The value of the smallest angle is

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°.