It can possess all five properties.

The description does not say that
heptagon has to be convex, i.e. all of its interior angles need not
be less than $180^{\circ}$. Since $(2 \timesĀ 7 - 4) \times 90
= 900$, the interior angles of all heptagons total $900^{\circ}$.
The creation of a heptagon with all the given conditions is
possible as the diagram shows. Notice that four of the interior
angles are acute and the other three are reflex angles.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.