  Let $\mathscr C$ be a Krull-Schmidt $(n+2)$-angulated category and $\mathscr
A$ be an $n$-extension closed subcategory of $\mathscr C$. Then $\mathscr A$
has the structure of an $n$-exangulated category in the sense of
Herschend-Liu-Nakaoka. This construction gives $n$-exangulated categories which
are not $n$-exact categories in the sense of Jasso nor $(n+2)$-angulated
categories in the sense of Geiss-Keller-Oppermann in general. As an
application, our result can lead to a recent main result of Klapproth.
