### Icosagram

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at the number of diagonals?

### Playground Snapshot

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

### LOGO Challenge - Following On

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

# Heptagon Has

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

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.