An equilateral triangle, square and regular pentagon all have the same side length. The triangle is drawn on the top edge of the square, and the pentagon is drawn on and below the bottom edge of the square. All of the edges match up exactly.

What is the sum of the interior angles of the resulting polygon?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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