Transcript Polygons and Their Angles - Broken Arrow Public Schools

Polygons and Their
Angles
1-6 and 6-1
Polygon: A closed figure. They have vertices, sides, angles, and
exterior angles.
You name a polygon by just listing its vertices in order around the polygon.
ABCDEF
One name for this polygon is _________________________
Diagonal: a segment connecting two NONconsecutive vertices of a polygon.
AC or AD or AE
Diagonal Example: __________________
Convex Polygons - polygons where no diagonal
goes outside the figure.
Concave Polygons - polygons where any diagonal goes
outside of the figure. Concave polygons “cave” in.
Classifying
Polygons
You can classify a polygon
by the number of sides it has.
YOU WILL BE EXPECTED
TO KNOW THESE!!
INTERIOR ANGLE SUM
THEOREM
The sum of the measures of the angles in a convex polygon
with n sides is (n - 2)180
Exterior Angle Sum
Theorem
The sum of the measure of the exterior angles of ANY
convex polygon, one at each vertex is 360
Example
Find the interior and exterior angle sums for each polygon:
1. quadrilateral (4-2)180 = 360
Exterior Angle sum is always 360
2. 12-gon
(12-2)180 = 1800
Ext. Angle Sum = 360
5. decagon
(10-2)180 = 1440
Ext. Angle Sum = 360
6. pentagon
(5-2)180 = 540
Ext. Angle sum = 360
3. hexagon
7. octagon
4. nonagon
8. 18-gon
(6-2)180 = 720
Ext. Angle Sum = 360
(9-2)180 = 1260
Ext. Angle Sum = 360
(8-2)180 = 1080
Ext Angle Sum = 360
(18-2)180 = 2880
Ext Angle Sum = 360
Example 2
Find the value of x
You should get x = 100
Since there are 5 sides, then the
interior angle sum is (5-2)180 or 540.
Then take 360 - 90 - 90 - 160 - 150 to
get x.
You should get 50
You know there are 4 sides, so
the interior angle sum is 360.
Take 360 - 60 and you get 300.
Then divide by 3 and each
angle is 100.
You should get x = 90
Do the same for the others. Count
the number of sides and figure
the interior angle sum. Then
subtract out the angles that
you already know.
Regular Polygons
Regular Polygons - a polygon that is BOTH
equilateral
AND equiangular
If you see the word REGULAR, it means the figure is special
and you can divide by the number of sides to get
individual angle measures
Example 3
For each REGULAR polygon, find the measure of
each interior angle and exterior angle.
13. triangle
Interior =(3-2)180 / 3 = 60
Exterior = 360 / 3 = 120
14. quadrilateral
Interior = (4-2)180 / 4 = 90
Exterior = 360 / 4 = 90
15. hexagon
16. decagon
Interior = (10-2)180 / 10 = 144
Exterior = 360 / 10 = 36
17. 15-gon
Interior = (15-2)180 / 15 = 156
Exterior = 360 / 15 = 24
Interior = (6-2)180 / 6 = 120
Exterior = 360 / 6 = 60
NOTICE: interior and
exterior angles add to
180!!!!
Example 4
How many sides does a regular polygon have
if the measure of each exterior angle is:
Just take 360 divided by each angle to get your answer
18. 60 6 sides
19. 1524 sides
20. 1203 sides
Example 5
How many sides does a regular polygon have if
the measure of each interior angle is:
Since the interior and exterior angles
Add to 180, find the exterior angle first!!!
21. 60
Interior angle is 60, so exterior angle is
180-60 = 120. Now do 360 divided by 120.
You should get 3.
22. 160
Interior angle is 160. 180-160 = 20, so exterior
angle is 20. Now do 360 divided by 20. You get 18
23. 144
Interior angle is 144. 180-144 = 36, so exterior
angle is 36. Now do 360 divided by 36. You get 10.
Have a great day!!