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Suppose such a polygon has n sides. Then the sum of the interior angles is (n-2)*180 degrees.

Since it is regular, each interior angle is (n-2)*180 / n degrees.

Thus (n-2)*180 / n = 100

(n-2)*180 = 100*n

180n - 360 = 100n

80n = 360

n = 4.5

Sorry, but you cannot have a polygon with 4.5 sides!

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Q: Can a regular polygon have interior angle measures of 100 degrees?
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