Question 75
A regular heptagon $ABCDEFG$ is given. The sides $AB$, $BC$, $CD$, $DE$, $EF$, $FG$ and $GA$ are called opposite to the vertices $E$, $F$, $G$, $A$, $B$, $C$ and $D$, respectively. If $M$ is an interior point of $ABCDEFG$, we say that a line through $M$ and a vertex of $ABCDEFG$ intersects the boundary of $ABCDEFG$ at a good point if this point is interior for the side which is opposite to the vertex. Prove that for every point $M$ the number of the good points is odd.