  In this paper, we study ideal approximation theory associated to almost
$n$-exact structures in extension closed subcategories of $n$-angulated
categories. For $n=3$, an $n$-angulated category is nothing but a classical
triangulated category. Moreover, since every exact category can be embedded as
an extension closed subcategory of a triangulated category, therefore, our
approach extends the recent ideal approximations theories developed by Fu,
Herzog et al. for exact categories and by Breaz and Modoi for triangulated
categories.
