What is the number of sides of a convex polygon if the sum of the measures of its interior angles is between 5800 and 6000?
a. name the polygon according to the number of side it has
b. find the exact sum of the measures of the interior angles
2007-10-08 01:31:55 · 3 answers · asked by Gothic Ayu 1 in Science & Mathematics ➔ Mathematics
If a polygon had n sides, then the sum of its interior angles = 180*(n-2).
If n=35, then the sum = 180+(35-2) = 5940.
a) triacontakaipentagon (35 sided polygon. Had to google this one :) )
b) 5940 degrees
2007-10-08 01:40:28 · answer #1 · answered by mathguru 3 · 0⤊ 0⤋
The general equation for the sum of the interior angles is
180(n - 2)
where n is the number of sides.
So...
5800 < 180(n - 2) < 6000
32.22222 < n - 2 < 33.33333
34.22222 < n < 35.33333
so... n = 35 (the only whole number between those two numbers.
a) It's a 35-gon. (I have no idea how to name it, sorry.)
b) 180(35 - 2) = 180(33) = 5940
2007-10-08 08:38:23 · answer #2 · answered by Mathematica 7 · 0⤊ 0⤋
Sum = 180(n-2) so n=35 sides
S=5940
2007-10-08 08:42:31 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋