Let $ABCD$ be a quadrilateral. Let $\{F\}=AB\bigcap CD$ and $\{E\}=BC\bigcap AD$. Then $AFCE$ is a complete quadrilateral.
The complete quadrilateral has four sides : $\overline{ABF}$, $\overline{ADE}$, $\overline{BCE}$, $\overline{DCF}$, and six angles: $A$, $B$, $C$, $D$, $E$, $F$.