$M+N$ is a closed subspaces of banach space iff $M^{\bot} +N^{\bot}$ is closed subspace of dual

Question

Let $X$ be a Banach space and let $M,N$ be closed subspaces of $X$. I want to prove that $M+N$ is a closed subspace iff $M^{\bot}+N^{\bot}$ is a closed subspace of $X^{\ast}$ (i.e, dual of $X$).

Any help would be appreciated. Thanks