  Let $\C$ be an $(n+2)$-angulated category with shift functor $\Sigma$ and
$\X$ be a cluster-tilting subcategory of $\C$. Then we show that the quotient
category $\C/\X$ is an $n$-abelian category. If $\C$ has a Serre functor, then
$\C/\X$ is equivalent to an $n$-cluster tilting subcategory of an abelian
category $\textrm{mod}(\Sigma^{-1}\X)$. Moreover, we also prove that
$\textrm{mod}(\Sigma^{-1}\X)$ is Gorenstein of Gorenstein dimension at most
$n$. As an application, we generalize recent results of Jacobsen-J{\o}rgensen
and Koenig-Zhu.
