what is the size of an exterior angle of a regular polygon with 180 sides.

Each exterior angle is 1 degree.

what is the size of an exterior angle of a regular polygon with 180 sides.   

The sum of the interior angles   

of a regular polygon is   

                                                   total  =  (n – 2)(180^o)   

                                                   where n is the number of sides  

The total for 180 sides is           

                                                   total  =  (180 – 2)(180^o)  

                                                   total  =  178 • 180^o  =  32,040^o   

That's the total.  Each angle

would be the total divided by  

the number of sides.     

                                                                                            32,040^o  

                                                   a single interior angle  =  ––––––––    

                                                                                               180   

                                                   a single interior angle  =  178^o     

I see now that I should have anticipated that answer and done it in my head. 

An exterior angle is 180^o minus the interior angle. Visualize extending a side   

beyond the angle.  A straight line contains 180^o   

                                                    exterior angle  =  180^o – 178^o  =  2^o   

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