What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio $3: 4: 5$?

Let

3x> angle exterior 1

4x> angle exterior 2

5x> angle exterior 3

we know that

The exterior angles of any polygon add up to 360 degrees

so

3x+4x+5x=360> 12x=360> x=30°

The largest of exterior angles is equal to the smallest of interior angles

so

the largest of exterior angles is 5x> 5*30=150°

the smallest of interior angles is 180°-150°=30°

therefore

the answer is

the smallest of interior angle measure 30 degrees