Warm Up
7.3 Formulas involving Polygons
Use important formulas that apply to
polygons
Sums of interior angles
Name
# of
sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
n-gon
n
# of
triangles
1
2
3
4
5
6
n-2
Work
1 (180)
2(180)
3(180)
4(180)
5(180)
6(180)
(n-2)(180)
Total
degrees
180
360
540
720
900
1080
T 55: Sum Si of the measure of
the angles of a polygon with n
sides is given by the formula
Si = (n-2)180
1
5
4
2
Exterior angles
3
Sum of interior <‘s = 3(180)
= 540
Sum of 5 supplementary <‘s = 5(180)
= 900
900 - 540 = 360
Total sum of all exterior <‘s = 360
T 56 : If one exterior angle is taken
at each vertex, the sum Se of the
measures of the exterior <‘s of a
polygon is given by the formula
Se = 360
T 57: The number of diagonals
that can be drawn in a polygon of
n sides is given by the formula
d = n(n-3)
Try: draw then do
the math!
2
In what polygon is the sum of the
measure of exterior <‘s, one per
vertex, equal to the sum of the
measure of the <‘s of the polygon?
Quadrilateral
360 = 360
In what polygon is the sum of the
measure of interior <‘s equal to
twice the sum of the measure of
the exterior <‘s, one per vertex?
Hexagon: 720 int. = 2(360) ext.
720 = (n-2)(180)
720 = 180n – 360
1080 = 180n
n=6