what is the formula to find the number of sides of the regular polygon with an interion angle measure of 60?
2006-10-08 04:09:12 · 3 answers · asked by hoopmaster1 1 in Science & Mathematics ➔ Mathematics
I don't know the formula but I sure now how to figure it out in a hurry. Imagine yourself driving around the polygon. At each vertex you need to turn a little. For an N sided polygons there are N truns. After you have gone all around, you have turned a total of 360 degrees so each turn is 360/N degrees. Your turns are not the internal angles of the polygon, but your turn plus the internal angel do make a straight line or 180 degrees so the internal angle (A) is 180 minus your turn angle:
A = 180 - 360/N = 180 * (1 - 2/N)
You can rearrange this then to make:
N = 360/(180 - A)
2006-10-08 05:29:45 · answer #1 · answered by Pretzels 5 · 0⤊ 0⤋
The formula for the interior angle of a regular polygon with n sides, in degrees, is
180(n-2)/n
or in radians,
pi - 2*pi/n.
Since 180(n-2)/n = 60 in this case, that means (n-2)/n = 1/3, or 3(n-2)=n. Now solve this for n: 3n-6=n, so 2n=6, meaning n=3. The polygon is an equilateral triangle.
2006-10-08 11:15:12 · answer #2 · answered by James L 5 · 0⤊ 0⤋
the total number of degrees of the internal angles in a polygon can be found from
D=(n-2)8180
the number of degrees in this polygon are
D=60n
so
60n=180(n-2)
60n=180n-360
-120n=-360
n=3
you have an equilateral triangle.
2006-10-11 19:11:00 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋