Since the exterior angle measures have the ratio $3:4:5$, they are $3x:4x:5x$ for some value of $x$. Each exterior angle is supplementary to an interior angle, so the measures of the interior angles of the triangles are $180^\circ - 3x$, $180^\circ - 4x$, and $180^\circ - 5x$. The sum of the interior angles of a triangle equals $180^\circ$, so we have
\[(180^\circ -3x) + (180^\circ - 4x) + (180^\circ - 5x) = 180^\circ.\]Simplifying this equation gives $-12x = -360^\circ$, so $x = 30^\circ$. Therefore, the smallest interior angle has measure $180^\circ - 5x = \boxed{30^\circ}$.
