Challenge Level

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.

This problem is taken from the UKMT Mathematical Challenges.

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