1. Polygons – Measurements of Angles
State the Name for each Polygon described
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 = 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. Find the value of x.
85
57
112 x