Download More with Polygons! - Aurora City Schools

Integrated Math 1 - 4/25/13
Learning Target: Different Angles in a Polygon
If a gallon of paint covers 450 ft2, how
many gallons must you buy to apply two
coats to seven rectangular walls, each
of which is 12 ft by 8 ft?
More with Polygons!
Polygons - many sided/angled figure
Regular Polygon - all sides and angles are congruent.
1
Common Polygons
Triangle:
3 sides/angles
Quadrilateral: 4 sides/angles
Pentagon:
5 sides/angles
Hexagon:
6 sides/angles
Heptagon:
7 sides/angles
Octagon:
8 sides/angles
Nonagon:
9 sides/angles
Decagon:
10 sides/angles
*after that we generally classify a polygon as a "___­gon" filling in the blank with the number of sides/angles.
ex. 15 sided figure is a 15­gon.
.
interior angle
exterior angle
The "interior angle sum" is the sum of all interior angles.
The "exterior angle sum" is the sum of all exterior angles.
.
2
Finding the interior angle sum in easy... just see how many triangles can be made by connecting verticies without overlapping.
A
E
B
180 x _____ = D
C
A
B
D
C
A
B
F
C
E
D
Formula:
.
Finding each interior angle of a regular polygon is
easy too...
Divide the total interior angle sum by the
number of angles. This gives the degrees for
each angle.
ex: 180 x 3 = 540 total degrees
540 ÷
=
degrees in each interior angle .
3
Exterior Angles
What is the relationship between interior and exterior angles?
ex:
108o
?
?
108o
o
? 108
Supplementary!
108o
So, to find exterior angles...
?
108o
180 ­ int angle
?
*What is the sum of these exterior angles?
.
Angles in a Regular Polygon
Polygon
# of Sides
Interior
Angle
Sum of
Int Angles
Exterior
Angle
Sum of
Ext Angles
Triangle
Quadrilateral
Pentagon
4
5