Ok i am in geometry and i need help with this problem its about Interior and Exterior Angles and finding. I've tried every way to figure out this problem and it won't work. The problem is: Find the number of sides of a regular polygon each of whoseinterior angle contains 120 degrees. Any help would be appreciated thanx
2006-11-18 08:31:04 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
use the equation [(n-2)*180]/n to find one of the angles of the polygon
n = the number of sides
[(n-2)*180]/n = 120
180n - 360 = 120n
60n = 360
n = 6
ANSWER
6 sides, or a hexagon
2006-11-18 08:41:20 · answer #1 · answered by trackstarr59 3 · 0⤊ 0⤋
Hopefully nobody decides to be too nice and give a straight answer. Take any polygon and make triangles to each vertex from the center, and what do you get? Isoceles triangles, right? Alright, start with two lines that give a 120 degree angle. If you bisect the angle, what do you get? Each angle will be 60 degrees, right? Do you see where I'm going? Probably not, but keep trying. If you actually draw this out on paper you'll have an easier time of seeing what the angles are doing.
Still on it? Well, here's another hint if you get stuck. If two angles of a triangle add up to 120 degrees, what is the third angle? Finally, all those angles in the center are going to add up to 360 degrees, as you can probably see, since they're the added angles of a circle, so how much of 360 degrees does that angle make?
2006-11-18 08:39:23 · answer #2 · answered by Jacob P 2 · 1⤊ 0⤋
Here is an easy way to do it. Since the EXTERIOR angles of a polygon always add up to 360, calculate the exterior angles' measure (they are supplementary to the interior ones, so do 180-120 = 60
Then just divide 360 by 60; that's how many angles and therefore how many sides
2006-11-18 08:34:15 · answer #3 · answered by hayharbr 7 · 0⤊ 0⤋
Here is an easy way to do it. Since the EXTERIOR angles of a polygon always add up to 360, calculate the exterior angles' measure (they are supplementary to the interior ones, so do 180-120 = 60
Then just divide 360 by 60; that's how many angles and therefore how many sides
2006-11-18 08:38:52 · answer #4 · answered by Pal G 2 · 0⤊ 0⤋
Here's how I do it. The sum of the interior angles of
a polygon is (n-2)180. For example in a triangle n is 3
so we get (3-2)180=180. A rectangle gives you (4-2)180=360
etc.
So when (n-2)180=120n (your example) then
180n -360=120n
180n -120n=360
60n=260
n=6
2006-11-18 08:48:52 · answer #5 · answered by albert 5 · 0⤊ 0⤋