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12,600 degrees -- and it doesn't matter whether the 72-gon is regular or not.

The sum of the exterior angles (from an extension of each side to the next) of any polygon is always 360 degrees. Therefore the sum of the interior angles is always (number of sides) * 180 - 360. 72 * 180 - 360 = 70 * 180 = 12,600.

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