2007-01-23 02:11:01 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The sum of the (interior) angles of a triangle is 180 and each time you add a side you add another 180. So
4 - 360
5 - 540
6 - 720
etc
n sides - (n-2) times 180
If you meant the exterior angles, they always add up to 360 no matter how many sides.
2007-01-23 02:14:20 · answer #1 · answered by hayharbr 7 · 0⤊ 1⤋
The sum of the interior angles in a polygon with n sides is 180º(n – 2).
therefore:
4 = 180*2 = 360
5 = 180*3 = 540
6 = 180*4 = 720
2007-01-23 02:18:44 · answer #2 · answered by yhwhlivesinme 2 · 0⤊ 0⤋
the general formula
Sum = 180(n-2) degrees
Explanation :Each side of the polygon form a triangle isoscele.
The sum of the angles on the side form an angle of the polygon. There are n triangles and the sum of the n angle with vertix at the center are 360 deg.
calling" a " the angle of the polygon and recalling that the sum of the angles iin a triangle is 180 deg you ge
sum +360=180*n
So sum = 180(n-2)
In a polygon of 9 sides this is 180*7 =1260 degrees
2007-01-23 05:37:22 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
.
The sum of all the interior angles of a polygon is very easy to calculate...
The formula for it is: (n-2)π or in other words (n-2) * 180º
- where n is the number of sides in the polygon
Let me derive this for your better comprehension...
Let our polygon have "n" sides...
Let's take a point , say O, within the polygon...
Now, using point O and each side of the polygon form a triangle such that O is the vertex opposite to the side...
You will have a total of n such triangles as you have n sides in the polygon...
Now, you must know that the sum of all the angles of a triangle comes to 180º... You will also know that angle covered by a complete circle is 360º... And these 360º are included in the sum of the angles of the n triangles, but, is not actually part of the polygon's angles...
So, now, the sum of all the angles of the polygon will be,
= The total of the sum of the angles of the 'n' triangles - 360º
= n * 180º - 360º
= (n - 2) * 180º
Hence, the sum of all the interior angles of a polygon is equal to = (n-2) * 180º or (n-2)π
.
2007-01-23 02:31:19 · answer #4 · answered by Preety 2 · 0⤊ 0⤋
sum of the angles = (number of angles -2)*180
4 = 360
5 = 540
6 = 720
7 = 900
8 = 1080
9 = 1260
10= 1440
2007-01-23 02:16:09 · answer #5 · answered by Anonymous · 0⤊ 0⤋
360
540
720
900
1080
1260
1440
2007-01-23 02:19:39 · answer #6 · answered by bartender1115 2 · 0⤊ 0⤋