A heptagon is a seven-sided polygon. What is the greatest number of the following properties that a single heptagon can possibly possess?
- Its interior angles add up to $900$ degrees
- It has exactly four acute interior angles.
- It has no obtuse interior angles.
- All its sides are equal.
- It has exactly one line of symmetry.
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.