If Each Exterior Angle Of A Regular Polygon Is 12 Degree, Find The No. Of Sides Of The Polygon. Any Suggestion?


4 Answers

Oddman Profile
Oddman answered
The exterior angle is the supplement of the interior angle. We know the sum of the interior angles is (N-2)*180 degrees for an N-sided polygon. Summing the interior angles, we get to the same conclusion Dragonfire came to: The sum of the exterior angles is always 360 degrees. Let N = the number of sides in your regular polygon.

Summing interior angles, we have ...
N(180-12) = (N-2)180 = 180N-360
360 = N(180 - (180-12)) = 12N
360/12 = 30 = N

Emma Grace Profile
Emma Grace answered
Ok! Let us considera 6-sided polygon.The interior angles of the polygon are named a,b,c,d,e and f while the exterior angles are named p,q,r,s,t and you.Make it like this:
  a+p=180 degrees  b+q=180 degrees
  c+r=180 degrees   d+s=180 degrees
  e+t=180 degrees   f+you=180 degrees
a+p+b+q+c+r+d+s+e+t+f+you=1080 degrees
(a+b+c+d+e+f)+(p+q+r+s+t+you), but we know that the sum of the interior angles of the polygon with 6-sides is 8 right angles I-e...720
Thus, 720+(p+q+r+s+t+you)=1080
By showing this method, the sum of the exterior angles of a polygon with 5 sides,7 sides or any no of sides can be shown to be equal to 360
In general,we have the following:
   the sum of the exterior angles of any polygon is 360Q0 Find the number of sides of a polygon whose interior angles are 156 each?
Solution:Each interior angle=156
ach exterior angle=180-156=24 degree
Now thw sum of the exterior angles is 360.
The number of sides,n,is given by nx24 =360
the polygon has 15 sides. Hope you got the point! :)
thanked the writer.
Anonymous commented
360/12 = 30! It has 30 sides cause the sum of all the exterior abgles in ANY POLYGON is always 360! Hope i helped

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