Symmetry and angle properties of polygons

a polygon is a plane figure with 3 or more straight edges as its sides (in other words, no circles. or weird blobs).

REGULAR POLYGONS:
the basics are as such: no. of sides = what polygon
i) 3 = equilateral triangle
ii) 4 = square
iii) 5 = pentagon
iv) 6 = hexagon
v) 7 = heptagon
vi) 8 = octagon
vii) 9 = nonagon
viii) 10 = decagon

(you'll realise that the front portion of the name can come out in chemisty too. like pentane. *coughs* but i'm talkin' math here, buddy. )

the formulaes are:
i) sum of interior (int.) angles (ang) of an n-sided polygon = (n - 2) x 180* (* = degrees)

eg: sum of int.ang of a triange = (3-2) x 180*
which is like duh since sum of all int.angs in a triangle = 180*

or eg. sum or int.ang of a nonagon = (9-2) x 180* = 1260*
(don't believe me? go draw, and figure why it's 1260*. this can apply to irregular polygons, so there's hope yet. yay. *deadpans* )


ii) sum of exterior(ext.)angs of an n-sided polygon = 360*
(if you don't know, go draw one and measure. mathematicians must have figured that since there is NO change no matter how many times they draw it, it just has to be like that. hence the formulae. note: it doesn't say regular polygon either. )


iii) each int.ang of a regular n-sided polygon = [(n-2) x 180*]/n
sorry, it's in fractions. the / = divided by.

eg: 1 int of a nonagon= [(9-2) x 1980*]/9 = 1260*/9 = 140*


iv) each ext.ang of an regular n-sided polygon = 360*/n

eg: ext.ang nonagon = 360*/9 = 40*


v) no of sides of a regular polygon = 360*/ (1 ext. ang)
eg: no. of sides of a regular polygon= 360*/40* = 9 sides = nonagon
(see? see?)


vi) 1 ext.ang + 1 int.ang = 180*
(aka angs on a stright line. but that's in another angles chapter.)

(If you don't believe it, go draw. then you get your ans. it's always like that, like how the sun rises from the east and sets in the west. not north. or south. and we won't have an icy atlantica and instead might get an icy singapore. if you still don't get it, too bad. )