SOLUTION: What is the sum of the interior angles of a (a) square, (b) pentagon, (c) hexagon, (d) octagon, (e) decagon, (f) 100-gon, and (g) 1000-gon

Algebra ->  Polygons -> SOLUTION: What is the sum of the interior angles of a (a) square, (b) pentagon, (c) hexagon, (d) octagon, (e) decagon, (f) 100-gon, and (g) 1000-gon      Log On


   



Question 946797: What is the sum of the interior angles of a (a) square, (b) pentagon, (c) hexagon, (d) octagon, (e) decagon, (f) 100-gon, and (g) 1000-gon
Found 2 solutions by MathLover1, Fombitz:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Sum_+of_+Interior_+Angles_+of_+a_+Polygon=+180%28n+-+2%29 where n = number of sides
so, the sum of the interior angles of a
(a) square is
n=4
Sum_+of_+Interior_+Angles_+of_+a_+square=+180%284+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+square=+180%282%29
Sum_+of_+Interior_+Angles_+of_+a_+square=+360
(b) pentagon
n=5
Sum_+of_+Interior_+Angles_+of_+a_+pentagon=+180%285+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+pentagon=+180%283%29
Sum_+of_+Interior_+Angles_+of_+a_+pentagon=+540


(c) hexagon
n=6


Sum_+of_+Interior_+Angles_+of_+a_+hexagon=+180%286+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+hexagon=+180%284%29
Sum_+of_+Interior_+Angles_+of_+a_+hexagon=+720

(d) octagon
n=8
Sum_+of_+Interior_+Angles_+of_+a_+octagon=+180%288+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+octagon=+180%286%29
Sum_+of_+Interior_+Angles_+of_+a_+octagon=+1080

(e) decagon,
n=10
Sum_+of_+Interior_+Angles_+of_+a_+decagon=+180%2810+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+decagon=+180%288%29
Sum_+of_+Interior_+Angles_+of_+a_+decagon=+1440

(f) 100-gon,
n=100
Sum_+of_+Interior_+Angles_+of_+a_+100-gon=+180%28100+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+100-gon=+180%2898%29
Sum_+of_+Interior_+Angles_+of_+a_+100-gon=+17640
(g) 1000-gon
n=1000
Sum_+of_+Interior_+Angles_+of_+a_+1000-gon=+180%281000+-+2%29
Sum_+of_+Interior_+Angles_+of_+a_+1000-gon=+180%28998%29
Sum_+of_+Interior_+Angles_+of_+a_+1000-gon=+179640


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles for a polygon is S=%28n-2%29180 where n is the number of sides.
So for a) N=4,S=%284-2%29180=2%28180%29=360
Do the others the same way.