Let M be a compact,
orientable, irreducible, ∂-irreducible, anannular 3-manifold with one component T of
∂M a torus. Suppose that r1 and r2 are two slopes on T. In this paper, we shall show
that if M(r1) is reducible while M(r2) contains an essential annulus, then
△(r1,r2) ≤ 2.