Such a polygon does not exist.
A polygon with n sides has 0.5*n*(n-3) diagonals
If there are 10 diagonals then
0.5*n*(n-3) = 10
which requires n2 - 3n - 20 = 0 which has no integer roots.
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It has 10 sides because using the formula 0.5*(102-30) = 35 diagonals
10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.
A polygon has as many angles as sides, so a polygon with 10 sides (decagon) would have 10 angles.
A diagonal line of a polygon is a line that joins any two vertices not already joined by a side. A polygon with n sides has n(n-3)/2 diagonals → a decagon has 10(10-3)/2 = 10 × 7 ÷ 2 = 35 diagonals
65. The number of diagonals in a polygon with n sides is given by: diagonals = n(n - 3) / 2 So for a triskaidecagon which has 13 sides n = 13 and: number_of_diagonals = 13(13 - 3) /2 = 13 x 10 / 2 = 65