34. Given that one of the interior angles of a triangle is $63^{\circ}$, and there is an exterior angle that is equal to one of the interior angles of the triangle, then the smallest interior angle of the triangle is $\qquad$.
Answer: $27^{\circ}$.
Solution: In $\triangle A B C$, let $\angle A=63^{\circ}$. Since an exterior angle of a triangle is greater than any non-adjacent interior angle, the condition “an exterior angle is equal to one of the interior angles of the triangle” implies that this exterior angle can only be equal to its adjacent interior angle, i.e., they are supplementary angles, and both the exterior angle and its adjacent interior angle are equal to $90^{\circ}$.
Assume this angle is $\angle B$. Therefore, the other angle
$$
\angle C=180^{\circ}-90^{\circ}-63^{\circ}=27^{\circ} \text {. }
$$

Thus, the smallest interior angle in the triangle is $27^{\circ}$.