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We consider Λ an artin algebra and n ≥ 2. We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander-Reiten component of Cn(proj Λ) with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in Cn(proj Λ) belong to such a category. For a finite dimensional hereditary algebra H over an algebraically closed field, we determine when an irreducible morphism has finite left (or right) degree and we give a characterization, depending on the degrees of certain irreducible morphisms, under which Cn(proj H) is of finite type.