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If n greater than or equal to 3, for how many values of n is the measure of an interior angle of a regular n-gon less than the measure of an exterior angle?

 

Ive only found one solution but that is 3, I feel I am missing something and there must be more possiblilties pls help

 Aug 7, 2020
 #1
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Interior and exterior angles sum to 180

 

each interior angle is    180 - 360/n

 

each exterior angle    is    180 - 180   + 360/n   = 360/n

 

 

SO the question asks     180 - 360/n  <  360/n

                                        180 < 720 / n

                                           n < 720/180

                                            n < 4                          

 Aug 7, 2020

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