1. Polygons – Measurements of Angles
Names of Polygons
3 Sides :
4 Sides :
5 Sides :
6 Sides :
7 Sides :
8 Sides :
9 Sides :
10 Sides :
n Sides :
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon

2. Finding the Sum of interior angles of any polygon
Shape Sum of interior angles
Triangle: °
Quadrilateral :
Pentagon
Hexagon
2 triangles = 360°
3 triangles = 540°
4 triangles = 720 °
n-gon = 180(n - 2)
Where n = number of sides

3. For any polygon – To find the sum of the interior angles use the formula:
Sum of interior angles = 180(n – 2)
Where n = # of sides
Ex. Find the sum of the interior angles for the following
a) Octagon b) 13-gon
180(n – 2)
180 (8 – 2)
180(6)
1080
180(n – 2)
180(13 – 2)
180(11)
1280

4. Ex. Find the value of x.
180(n – 2)
180(5 – 2)
180(3)
540 x
x = 540
x = 540
x – 418 = 540 – 418
x = 122

5. Regular Polygon : All angles are equal
Ex. Find the measure of an interior angle of a regular hexagon.
180(n – 2)
180(6 –2)
180(4)
720
720 6
120
One interior angle of regular hexagon is 120

6. Exterior Angle: an angle on the outside of a polygon, formed by extending sides of polygon.
To find the measure of an Exterior angle of a polygon:
1) Find the measure of the supplemental interior angle
2) Write equation : Int. + ext. = 180
Ex. Find value of x 1.
x = 180
x – 103 = 180 – 103
x = 77 x
103

7. 2.
105 
75  x
x + 75 = 180
x + 75 – 75 = 180 – 75
x = 105

8. x
78
104
60 
x + 78 = 180
x + 78 – 78 = 180 – 78
x = 102

9. Find the measure of one exterior angle of a regular hexagon.
First – Find measure of one interior angle
Second - find exterior angle
x = 180
x – 120 = 180 – 120
x = 60

10. Find the measure of one exterior angle of a regular pentagon.
First – Find measure of one interior angle
Second - find exterior angle
x = 180
x – 108 = 180 – 108
x = 72

11. Sum of ALL EXTERIOR angles of a CONVEX polygon = 360
NOTE:
Sum of ALL EXTERIOR angles of a CONVEX polygon = 360
Ex. Find value of x
68 
81
90 x
x = 360
x = 360
x – 318 = 360 – 318
x = 42

12. NOTE:
Sum of ALL EXTERIOR angles of a CONVEX polygon = 360
Ex. Find value of x
75 x
104 
103
x = 360
x = 360
x = 360 – 282
x = 78

13. To find the measure of an Exterior angle of a polygon:
1) Find the measure of the supplemental interior angle
2) Subtract from 180 to find exterior angle
Ex.
115
x = 180
x –115 = 180 – 115
x = 65 x

14. Find the value of x.
85
57
112 x

15. Four things poison a team faster than anything else: arrogance, lack of communication, “me-first” vs. “we-first,” and jealousy/cynicism.