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

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

thanked the writer.
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
p+q+r+s+t+you=360
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
n=360/24=15
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 