Question 564681
The sum of the degrees in an n-gon is 180(n-2), so for a regular polygon, the interior angle measure will be 180(n-2)/n. Therefore, we have


*[tex \LARGE 100 \le \frac{180(n-2)}{n} \le 149]


*[tex \LARGE 100n \le 180n - 360 \le 149n]


The "first" inequality yields *[tex \LARGE 80n - 360 \ge 0 \Rightarrow 80n \ge 360 \Rightarrow n \ge 4.5].


The "second" inequality yields *[tex \LARGE 31n \le 360 \Rightarrow n \le 11.61...]


Therefore, n is between 4.5 and 11.61; the only integer values of n that satisfy are 5, 6, ..., 11, or seven values.