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The formula for the size of the interior angle for a regular polygon is 180°(n-2)/n, where n is the number of edges, i.e. a whole number. If we set this equal to 80° then we get 180°(n-2)/n=80°
180°n-360°=80°n
100°n=360°
n=3.6
which isn't a whole number. So no regular polygon can have an interior angle of size 80°.

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Q: Why cant a regular polygon have interior angles measuring 80 degrees?
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