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

 Jun 28, 2023
 #1
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Each exterior angle is 1 degree.

 Jun 28, 2023
 #2
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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)(180o)   

                                                   where n is the number of sides  

 

The total for 180 sides is           

                                                   total  =  (180 – 2)(180o)  

                                                   total  =  178 • 180o  =  32,040o   

 

That's the total.  Each angle

would be the total divided by  

the number of sides.     

                                                                                            32,040o  

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

                                                                                               180   

 

                                                   a single interior angle  =  178o     

 

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

 

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

beyond the angle.  A straight line contains 180o   

 

                                                    exterior angle  =  180o – 178o  =  2o   

.

 Jun 29, 2023

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