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In short:

The Pentagon

In Long:

The formula for the number of diagonals is

(x*(x-3))/2

So if you make that equal to x you get 5.

(x(x-3))/2=x

(x^2-3x)/2=x

x^2-3x=2x

x^2-5x=0

x=0 or x-5=0

x=0 or x=5

x=5

Because there is no polygon with 0 sides and the pentagon is defined as a polygon with 5 sides, the pentagon is the only regular polygon with the same amount of diagonals as it has sides.

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Q: What polygon has the same number of diagonals as it has sides?
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