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Integral Polygons

Age 11 to 14 Short Challenge Level:

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees.

What is the greatest number of sides the polygon could have?
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.