2006-06-07 07:23:34 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
36 degrees.
The formula is 360/n where n is the number of sides.
2006-06-07 07:26:46 · answer #1 · answered by Arbitrage 7 · 1⤊ 0⤋
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.
2006-06-07 08:45:35 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
The angles of any polygon have to add up to 180. For example, an equilateral triangle has 3 60 degree angles. So as long as all the angles are the same, and there are ten of them, they're all 18 degrees, or 162 from the outside.
2006-06-07 07:50:32 · answer #3 · answered by Beardog 7 · 0⤊ 0⤋
144? lol, it's been toooooo long since I took Geometry! :)
Edited to add....I thought 36 at first, but isn't that the INTERIOR angle?
2006-06-07 07:27:00 · answer #4 · answered by Anonymous · 0⤊ 0⤋