1. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Chapter 4.7
Polygons and Angle Measure
Polygons are named for the number of sides
they have.
3 sides = triangle 8 sides = octagon
4 sides = quadrilateral 9 sides = nonagon
5 sides = pentagon 10 sides = decagon
6 sides = hexagon n sides = n-gon
7 sides = heptagon

2. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Vocab
Vertex ­ intersection of
two sides VERTEX
Diagonal ­ segment between
two non­consecutive DIAGONAL
vertices
Key Vocab
REGULAR
A polygon is regular if it is equilateral
AND equiangular
Name the following shapes by the number of sides.
Are these shapes regular?
Example:
What is the perimeter of a regular
nonagon with a side length of 5 cm?

3. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
CONVEX vs. CONCAVE
Convex ­ the diagonals are INSIDE the polygon
Concave ­ part of the diagonals are OUTSIDE of the polygon
By drawing in all of the diagonals
from a vertex in a convex polygon,
we can cut the shape into triangles

4. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
How many diagonals can be drawn
from a vertex in a convex polygon?
# of sides # of Diagonals # of Triangles
How many DIAGONALS can be drawn in an n­sided polygon?
How many TRIANGLES are in an n­sided polygon?
If a polygon has n sides, we can
draw n­2 triangles inside of it.
5 sides
3 triangles
If each of these triangles has
180 degrees.

5. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
IMPORTANTE
If a convex polygon has n sides,
then the sum of interior angles is:
(n ­ 2) 180
Example: (n ­ 2) 180
Find the sum of interior angles for
the following convex polygons
Hexagon Heptagon
Octagon Pentagon
Decagon
Example
What is the measure of ONE
interior angle of a regular pentagon?
Sum of interior angles
(5 ­ 2) 180
3 180
5400
The measure of ONE angle is:
540 ÷ 5 = 1080
Example:
What is the measure of ONE
interior angle of a regular hexagon?

6. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
The sum of exterior angles for ANY
convex polygon is ALWAYS 3600
t
x
t + x + y + z + w = 360
w y
z
Example:
Find the sum of exterior angles for
the following convex polygons
Hexagon Heptagon
Octagon Pentagon
Decagon
Example:
What is the measure of ONE
exterior angle of a regular heptagon?

7. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Solve for x
2x
1050
750 x
350
Solve for n
n0
1130 370
n0

8. Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Formula Recap
Sum of Interior <'s Measure of ONE Interior <
(n­2) x 180 (n­2) x 180
n
Sum of Exterior <'s Measure of ONE Exterior <
3600 3600
n
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