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There has been a lot of criticism from the programming industry about students graduating without being taught "critical thinking", instead they are being told how to put a program together in Java. ...

You said that this problem has been bugging you for a while now (so I'm assuming that it was a while ago you did this question - i.e. You are no longer getting marked on this, right?)

Sounds like homework to me - This is ok, but you are going to have to provide your own solution

What have you attempted to "//Check if valid polygon"?