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Using the diagonal formula when n is number of sides :-

If: 0.5*(n^2-3n) = 189

Then multiplying both sides by 2 and subtracting both sides by 2*189

So: n^2-3n-378 = 0

Solving the above quadratic equation gives n a positive value of 21

Sum of interior angles: (21-2)*180 = 3420 degrees

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โˆ™ 2016-04-20 13:01:40
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Q: What is the total sum of its interior angles of a polygon that has 189 diagonals showing work?
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