Let $X$ be a Banach space, and let $X'\subset X$ - its subspace. Then the following propositions are true:

1. $X'$ is closed, $X/X' \cong \ell_1 \Rightarrow X'$ is complementary;
2. $X' \cong \ell_\infty \Rightarrow X'$ is complementary.

The first proposition, as it seems, can be continued to the case of $\ell_p$, if the case of $\ell_1$ is at least true.

For the second one there is an option to try using Hahn-Banach theorem, as we do the same for proof of finite-dimensional subspaces.