1. Do Now…… 1. A triangle with a 90° angle has sides that are 3 cm, 4 cm,
and 5 cm long. Classify the triangle by its sides and angles.
Use the diagram for Exercises 2–6.
2. Find m  3 if m 2 = 70 and m 4 = 42.
3. Find m 5 if m  2 = 76 and m  3 = 90.
4. Find x if m  1 = 4x, m  3 = 2x + 28, and m  4 = 32.
5. Find x if m  2 = 10x, m  3 = 5x + 40, and m  4 = 3x – 4.
6. Find m  3 if m  1 = 125 and m  5 = 160.

2. Section 4 Polygons Objectives: To classify Polygons
To find the sums of the measures of the interior & exterior s of Polygons.

3. Polygon: A closed plane figure. w/ at least 3 sides (segments)
The sides only intersect at their endpoints
Name it by starting at a vertex & go around the figure clockwise or counterclockwise listing each vertex you come across.

4. Which of the following figures are polygons?No
yes No

5. Name Polygons By Their:
Classify Polygons
Name Polygons By Their:
Vertices
Start at any vertex and list the vertices consecutively in a clockwise direction (ABCDE or CDEAB, etc)
Sides
Name by line segment naming convention
Angles
Name by angle naming convention
A, B, C, D, E

6. II. Also classify polygons by their Shape
a) Convex Polygon – Has no diagonal w/ points outside the polygon. E A B C D
b) Concave Polygon – Has at least one diagonal w/ points outside the polygon.
* All polygons are convex unless stated otherwise.

7. Special Polygons: Equilateral Polygon – All sides are .
Equiangular Polygon – All s are .
Regular Polygon – Both Equilateral & Equiangular.

8. I. Classify Polygons by the number of sides it has.3 4 5 6 7 8 9 10 12 n
Name
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
N-gon
Interior  Sum

9. III. Polygon Interior  sum
4 sides
2 Δs
2 • 180 = 360
4 sides
2 Δs
2 • 180 = 360
Each Interior --
Each Exterior--
Sum of exterior

10. 5 sides
3 Δs
3 • 180 = 540
Each Interior --
Each Exterior--
Sum of exterior

11. 6 sides
4 Δs
4 • 180 =
Each Interior --
Each Exterior--
Sum of exterior

12. 8 sides
6 Δs
6 • 180 =
Each Interior --
Each Exterior--
Sum of exterior

13. So……What’s the pattern?
Th(3-9) Polygon Angle – Sum Thm
S = (n -2) 180
Sum of Interior 
# of sides

14. So……What did you notice about the exterior angles?
The sum of the measures of the exterior s of a polygon is 360°. 1 2 3 4 5
m1 + m2 + m3 + m4 + m5 = 360
For Regular Polygons
= measure of one exterior 
The interior  & the exterior  are Supplementary.
Int + Ext = 180

15. Example #1
Find the interior angle sum.
a. 13-gon b. decagon

16. Example #2
How many sides does each polygon have if its interior angle sum is:
a  b 

17. Example #3
Find x.

18. Example #4
Find y.

19. Example #5
Find x.

20. Example #6
Find x.

21. Example #7
Find x.

22. Example #8
How many sides does each regular polygon have if its exterior angle is:
a. 120 b. 24

23. Example #9
How many sides does each regular polygon have if its interior angle is:
a. 90 b. 144