Thomas R. answered • 05/15/18
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Mark already demonstrated how easily you can calculate the answer, but I would like to throw in a memorization technique that my students always like.
Imagine you divide any N-gon into a series of triangles. That is, place a point in the center and draw as many triangles as there are sides. Every triangle has 180 degrees, so you simply multiply by the number of sides. But wait -- look at all of the angles you placed in the center that weren't part of the interior angles! They form a circle, which has 360 degrees. That's the same as 2 times 180, which is why Mark took two from the N and THEN multiplied by 180. So: you can just remember N triangles minus circle, or sides minus 2 times 180.
It makes a lot more sense with a polished drawing...
