Transcript Polygons

POLYGON:
Origin:
Greek “Poly-” meaning “many” and
“-gon” meaning “angle”
Definition:
a 2-dimensional, closed, shape
made of three or more straight
lines.
THE BASIC POLYGONS – PART 1
# of Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
Picture
Sum of Interior
THE BASIC POLYGONS – PART 2
# of Sides
Name
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
Picture
Sum of Interior
THE BASIC POLYGONS – PART 3
# of Sides
Name
12
dodecagon
n
n-gon
Picture
Sum of Interior
SUM OF THE INTERIOR
We can find the sum of the interior angles of any
polygon using the formula
Sum = 180(n-2)
n = the number of sides
Back to
the chart
THE BASIC POLYGONS – PART 1
# of Sides
Name
Picture
Sum of Interior
3
Triangle
180°
4
Quadrilateral
360°
5
Pentagon
540°
6
Hexagon
720°
THE BASIC POLYGONS – PART 2
# of Sides
Name
Picture
Sum of Interior
7
Heptagon
900°
8
Octagon
1080°
9
Nonagon
1260°
10
Decagon
1440°
THE BASIC POLYGONS – PART 3
# of Sides
Name
Picture
Sum of Interior
12
dodecagon
1800°
n
n-gon
180(n-2)°
THE ALGEBRA OF SUM OF THE INTERIOR
Find the value of x.
(4x) + 113 + (2x + 9) + (3x + 8) + 113 = 540
113°
X = 33
MORE INTERIOR ANGLE STUFF
1. The sum of the interior angles of a polygon is
1620 degrees. What is the name of the
polygon?
11-gon
We’ll know tomorrow
SUM OF THE EXTERIOR
The sum of the exterior angles of a polygon is
simple … it always equals
360°
A SINGLE EXTERIOR ANGLE
1. Find the measure of an exterior angle of a
regular heptagon. Round to the nearest
tenth if necessary.
51.4°
INTERIOR AND EXTERIOR
What is the relationship between an
individual interior and exterior
angle?
They are supplementary
MORE ALGEBRA
Find the value of x.
x + 138 + 2x + 100 + 110 = 540
138°
X = 64
100°