SOLUTION: how many regular polygons have an interior angle that measures between 100 and 149 degrees?
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Question 564681: how many regular polygons have an interior angle that measures between 100 and 149 degrees?
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
how many regular polygons have an interior angle that measures between 100 and 149 degrees?
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The exterior angles are between 31 and 80 degrees.
# of sides = 360/ext angle
360/32.7272 = 11 sides
360/36 = 10 sides
360/40 = 9 sides
360/45 = 8 sides
360/51.42 = 7 sides
360/60 = 6 sides
360/72 = 5 sides
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7 polygons
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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
}{n} \le 149)
The "first" inequality yields 
.
The "second" inequality yields 
Therefore, n is between 4.5 and 11.61; the only integer values of n that satisfy are 5, 6, ..., 11, or seven values.
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