Uniqueness of an embedded body extension in an algebraic closure

Question

Let K be a field and $\Omega$ be a cloture ajgebre of field K. We consider $L/K$ and $L'/K$ are two finite extension of field such that $L\subset \Omega$ and $L'\subset \Omega$ such that $\deg(L/K)=\deg(L'/K)$. Can we say that $L=L'$?