1. Two-Dimensional Figures
Polygons
&
Angles of Polygons

2. Identify and name polygons.
Find the sum of interior angles and a single interior angle of a regular polygon.
Find the sum of exterior angles and a single exterior angle in a convex polygon.
polygon
concave
convex
n-gon
Regular polygon

4. Number of Sides
Polygon 3
triangle 4
quadrilateral 5
pentagon 6
hexagon 7
heptagon 8
octagon 9
nonagon 10
decagon 12
dodecagon n
n-gon

5. Tetracontakaihexagon
What is an 46 sided figure called?
Hint- go to the website
The answer is…
Tetracontakaihexagon

6. Convex or Concave Polygons

7. Regular Polygon is… A convex polygon where: 1. All sides are congruent
2. All angles are congruent

8. Regular Hexagon Is it convex? All sides congruent?4
120°
120° 4 4
Yes
All sides congruent?
120°
120° 4 4
Yes
120°
120° 4
All angles congruent?
Yes
It’s a regular hexagon!

9. A Name the polygon?
quadrilateral
B Is it convex or concave?
convex
C Is it regular or irregular?
irregular

10. A Name the polygon?
nonagon
B Is it convex or concave?
concave
C Is it regular or irregular?
irregular

11. Interior Angle Sum (must be convex polygon)
Interior Angle Sum Practical Method
Triangle
Quadrilateral
Pentagon
Hexagon
180°
180°
180°
180°
180°
180°
180°
180°
180°
180°
Interior Angle Sum
180°
360°
540°
720°

12. Interior Angle Sum (must be convex polygon)
S = mA + mB + mC + mD + mE + mF
S = 180(n – 2) A B
S = 180(6 – 2) F C
S = 180(4)
S = 720° E D

13. Interior Angle Sum Example (must be convex polygon)
S = 180(n – 2)
S = 180(5 – 2)
S = 180(3)
S = 540°

14. Single Interior Angle of a Regular Polygon (must be convex polygon)
x = 180(n – 2) n
x = 180(6 – 2) A B
120°
120°
x = F C
120°
120°
120°
120°
x = 120° E D

15. Single Interior Angle of a Regular Polygon (must be convex polygon)
x = 180(n – 2) n
x = 180(3 – 2)
x =
x = 60°

16. Exterior Angle Sum (must be convex polygon)
60°
120°
60°
90°
90°
60°
Hexagon
Quadrilateral
Triangle
90°
60°
120°
90°
120°
60°
60°
Always add up to 360°

17. Single Exterior Angle of a Regular Polygon
60°
120°
60°
90°
90°
60°
Hexagon
Quadrilateral
Triangle
90°
60°
120°
90°
120°
60°
60°
120°
90°
60° 3 4 6

18. Given regular nonagon ABCDEFGHJ.
A Exterior Angle Sum?
360°
B. Single Exterior Angle?
360/9= 40°
(9 – 2)180 = 1260°
(n - 2)180 =
C Interior Angle Sum?
D. Single Interior Angle?

19. Multiply both sides by n
ALGEBRAIC METHOD
The measure of an interior angle of a regular polygon is Find the number of sides in the polygon.
135 = 180(n – 2) n
Multiply both sides by n
135n = 180(n – 2)
135n = 180n – 360
0 = 45n – 360
360 = 45n
8 = n
Answer: The polygon has 8 sides.

20. = 8 sides 135˚ 45˚ OFF the CHAIN METHOD
The measure of an interior angle of a regular polygon is Find the number of sides in the polygon.
= 8 sides
135˚
45˚

21. The measure of an interior angle of a regular polygon is 144
The measure of an interior angle of a regular polygon is Find the number of sides in the polygon.
A. 12
B. 9
C. 11
D. 10 A B C D

22. Find the measure of each interior angle.60 3x x
180
180 60 60
How many sides? 5
Find interior angle sum =
180(5 – 2)=
180(n – 2)
540
540
= 3x + 3x + x + x + x
540 = 9x
60 = x

23. Find the value of x. A. x = 7.8 B. x = 22.2 C. x = 15 D. x = 10 A B C

24. All of the diagonals from one vertex are drawn
for the regular polygons in the table to the right.
Fill in the table in order to find a pattern.
How many triangles are formed by drawing
all of the diagonals from one vertex of a
23-sided polygon?
A 19 triangles
B 20 triangles
C 21 triangles
D 23 triangles