2. In an acute $\triangle A B C$, the measures of the three interior angles are prime numbers, and the length of the shortest side is 1. The number of non-congruent triangles that satisfy these conditions is ( ).
(A) 1
(B) 2
(C) 3
(D) More than 3
2. A.

Let the measures of the three interior angles be $x$, $y$, and $z$ degrees. Then $x$, $y$, and $z$ are prime numbers, and $x + y + z = 180$. Therefore, at least one of $x$, $y$, and $z$ must be an even prime number. Without loss of generality, let $x$ be the even prime number. Then $x = 2$. Thus, $y + z = 178$.
Assume $y \leqslant z$. Then $z \geqslant 89$.
Since $\triangle ABC$ is an acute triangle, $z < 90$. Therefore, $z = 89$, and $y = 89$.
Upon verification, $x = 2$, $y = 89$, and $z = 89$ meet the conditions.
Given that the length of the shortest side is 1, there is only 1 triangle that meets the conditions.