Suppose $K$ is a compact convex set in $\mathbb R^n$. Prove that every $x\in K$ is a convex combination of at most $n+1$ extreme points of K.
I know that in $\mathbb R^n$ if $E\subset \mathbb R^n$ then for any $x\in co(E)$, $x$ lies in the convex hull of some subset of E which contains at most $n+1$ points and also by $Krein-Milman ~Theorem$ we know that $K= \overline{co}(E(K))$ but i am not able to linkup these two statements.
Any type of help will be appreciated. Thanks in advance.