Although my knowledge maybe not correct, but I will state it nonetheless;
"Delaunay triangulation maximizes the minimum angle among all triangulation"
"Every triangulation of regular n-gon satisfies Delaunay condition, as no point is in interior of circumcircle of any triangle formed, therefore they are all valid Delaunay triangulation."
Then, If I am not mistaken, does every triangulation of regular n-gon have same Inf angle, because they all maximizes the minimum angle, and they are all Delaunay?
Every angle is opposite an edge connecting two vertices of the $n$-gon. It equals half the angle from one vertex to the centre to the other vertex, so is a multiple of $\pi/n$. The smallest angle is always $\pi/n$.