Problems

Let $ABCDE$ be a regular pentagon. The point $G$ is the midpoint of $CD$, the point $F$ is the midpoint of $AE$. The lines $EG$ and $BF$ intersect at the point $H$. Find the angle $EHF$.

A paper band of constant width is tied into a simple knot and tightened. Prove that the knot has the shape of a regular polygon.