what is the measure of one of the exterior angles of a regular polygon with ten sides?

Answer 1

An *exterior* angle for a polygon is formed by extending one side of the polygon from one if its endpoints. The exterior angle and interior angle are therefore supplementary. If you extend each side of a polygon to form one exterior angle at each vertex, you get a set of exterior angles as shown in the attached diagram.
http://www.geom.uiuc.edu/~dwiggins/pict09.GIF

Be careful because some people have a mistaken definition of exterior angles and assume it is the full obtuse angle, but it isn't.

By theorom, the exterior angles in a convex polygon always add up to 360 degrees. A regular 10-sided polygon is one example of a convex polygon, so its exterior angles would also add up to 360 degrees. Because all the angles are equal in a regular polygon you would have:

360 / 10
= 36 degrees

So with a regular decagon (10-sided polygon), each exterior angle would be 36 degrees.

Answer 2

The formula to calculate the sum of the interior angles is (n-2)*180 where n is the number of sides on the polygon. Therefore the interior angles total 1,440.
Divide that by 10 to find out how much 1 interior angle is and you get 144 degrees. Subtract that from 360 and you get 216 which is the exterior angle.
**I stand corrected, I forgot the definition of an exterior angle. It should be 180 minus 144 which is 36 not 216. Oopsy.

Answer 3

for a regular polygon, the external angle is


in your case:



Edit: **** For Bandf ****

You are right, I have different idea of external angle (ext=360-internal) . What you explained is what I know as "turn angle". So turn angles for any "regular" polygon


Regards

Answer 4

The sum of the interior angles of a decagon is 1440 degrees. That means each interior angle is 144 degrees, and each exterior angle is (180-144) or 36 degrees.

Answer 5

180*10=1800..thats the interior...now the outside 4 one would be 180-10x=0
/10 /10
x=18