Question 1151067
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Regular octagon is a regular 8-gon (8 vertices, 8 sides).


The exterior angle of the regular octagon is  360 degrees divided by 8, i.e.

    {{{360/8}}} = 45 degrees.


Twenty eight times 45 degrees is  1260 degrees.


Thus the sum of interior angles of the polygon is  1260 degrees.


Using formula for the sum of the interior angles of a n-gon, you have this equation


    (n-2)*180 = 1260  degrees,   or


    n - 2 = 1260/180 = 7.


Hence,  n = 7+2 = 9, and the polygon is 9-gon (nonagon).     <U>ANSWER</U>
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Solved.