Question 560250: is it possible to have a polygon whose sum of interior angle is
(1) 7 right angle
(2) 4500
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for the sum of the interior angles of a polygon is:
S = 180 * (n-2)
if n = 3 (triangle), then S = 180 * (3-2) = 180
if n = 4 (quadrilateral), then S = 180 * (4-2) = 360
from the formula for S, we can derive the formula for n as follows:
S = 180 * (n-2)
divide both sides of this equation by 180 to get:
S / 180 = n-2
add 2 to both sides of this equation to get:
n = (S/180) + 2
for the triangle, we get:
n = (180/180) + 2 which equals 1 + 2 which equals 3.
for the quadrilateral, we get:
n = (360/180) + 2 which equals 2 + 2 which equals 4.
if the sum of the interior angles is 4500, then the formula becoms:
n = (4500/180) + 2 which becomes:
n = 25 + 2 which becomes:
n = 27
i'm not sure what you mean by 7 right angle.
if you mean 7 * a right angle, then the sum would be 7 * 90 = 630 degrees.
the formula becomes:
n = (630/180) + 2 which becomes:
n = 3.5 + 2 which becomes:
n = 5.5
since n has to be an integer, the sum of angles equal to 630 degrees would not be possible.
if n is 5, the sum is 3 * 180 = 540 degrees.
if n is 6, the sum is 4 * 180 = 720 degrees.
|
|
|
