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In this paper, we study the notion of approximate biprojectivity and left φ-biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L1K implies that K is compact. Moreover, we investigate left φ-biprojectivity of certain hypergroup algebras, namely, abstract Segal algebras. As a main result, we conclude that (with some mild conditions) the abstract Segal algebra B is left φ-biprojective if and only if K is compact, where K is a hypergroup. We also study the approximate biflatness and left φ-biflatness of hypergroup algebras in terms of amenability of their related hypergroups.