  Xiao and Zhu has shown that if $\cal C$ is a locally finite triangulated
category, then the Auslander-Reiten triangles generate the relations for the
Grothendieck group of $\cal C$. The notion of $(d +2)$-angulated categories is
a "higher dimensional" analogue of triangulated categories. In this article, we
show that if A $(d+2)$-angulated category $\cal C$ is locally finite if and
only if the Auslander-Reiten $(d+2)$-angles generate the relations for the
Grothendieck group of $\cal C$. This extends the result of Xiao and Zhu, and
gives the converse of Xiao and Zhu's result is also true.
