Integral Polygons

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?
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Problem



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.