A polygon of n sides can have n-1 diagonal from each vertex. From n vertices, the polygon can have n(n-1)/2 diagonals. The number has to be divided by 2 because we have counted the diagonal from both sides.
So using the formula
d(n)=n(n-1)/2
you can find n.
Hint: n is between 5 and 15.
A polygon has d diagonals. If the polygon had one more side, it would d + 10 diagonals. How many sides does the polygon have?
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