SOLUTION: Can someone pls help with steps to answer the below question: Name the polygon whose sum of the interior angle measures is twenty eight times the measure of one exterior angle o

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Question 1151067: Can someone pls help with steps to answer the below question:
Name the polygon whose sum of the interior angle measures is twenty eight times the measure of one exterior angle of a regular octagon
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Name the polygon whose sum of the interior angle measures is twenty eight times the measure of one exterior angle of a regular octagon
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Step 1, find the exterior of a regular octagon.
Ext angle = 360/n where n = # of sides.
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Step 2, multiply that by 28.
Call it Int degrees.
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Step 3, use the sum of the interior angles = (n-2)*180 degs.
Solve for n
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PS Not all regular polygons have names.
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
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.

     = 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).     ANSWER

Solved.



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