The difference between the measure of an interior angle and an exterior angle of a regular polygon is 100°. What is the number of sides of the polygon?
9
For a regular polygon with \(n\) sides, exterior angle \(= \frac{360°}{n}\) and interior angle \(= 180° - \frac{360°}{n}\).
Difference between interior and exterior angle: \(\left(180° - \frac{360°}{n}\right) - \frac{360°}{n} = 100°\).
So \(180° - \frac{720°}{n} = 100°\), giving \(\frac{720°}{n} = 80°\).
So \(n = \frac{720}{80} = 9\).
Hence, the polygon has 9 sides.
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