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The interior angle of a pentagon is 108 degrees. We can figure this out by taking the number of sides, 5, subtracting 2, to get 3, and then multiplying by 180 to get 540, which is the sum of all the interior angles. Therefore, each interior angle is equal to 108. The inside of this hypothetical ring will have the shape of a n-gon, with n sides. We can call the measure of the interior angle x. The interior angle of the n-gon plus two times the interior angle of the pentagon equals 360 degrees. We can solve to get x = 360 - 108*2, which simplifies to n = 44. Therefore, each interior angle of this n-gon is 44. We can use the same formula as we did in the beginning to find the number of sides of this n-gon. So, we have [180(n-2)]/n = 44. So, we have 180n-360 = 44n, to get n = 360/130. A polygon cannot have a fraction of a side, so this is not possible.