George is thinking about a regular polygon. If he takes the number of diagonals in the polygon and adds the number of degrees in an exterior angle, the result is 84. What kind of polygon is George thinking about?
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I've gotten to n(n-3)/2 + 360/n = 84. Then I was unsure what to do but I multiplied both sides by 2n to get rid of denominators and got n^2(n-3) + 720 = 168n which is the same as n^3 - 3n^2 - 168n + 720 = 0 but I can't factor that.
Dodecagon (12 sides). Exterior angle of regular 12-gon is 30 and number of diagonals is 54. See the following link for solutions to Mr. Id's (above) equation.
How did you do that algebraically though. I mean sure you can guess and check...