The Krein Milman theorem

Question

I am trying to understand the Krein Milman theorem from Rudin's Functional Analysis, Second Edition (page no 75). It has been shown that if $K $ is a compact convex subset of a topological vector space $X$, then every compact extreme set $S$ has a non empty intersection with the set of all extreme points $E (K)$ of $K$. Herefrom how can I say that $K$ is a superset of the closure of the convex hull of $E (K ) $?