1. Polygons
Geometry Unit 2

2. Polygon:
Origin: Greek “Poly-” meaning “many” and “-gon” meaning “angle” Definition: a 2-dimensional, closed, shape made of three or more straight lines.

3. NOT A POLYGON!
POLYGON!
POLYGON!
NOT A POLYGON!
POLYGON!
POLYGON!

4. The BASIC Polygons – Part 1
# of Sides
Name
Picture
Sum of Interior 3 4 5 6
Triangle
Quadrilateral
Pentagon
Hexagon

5. The BASIC Polygons – Part 2
# of Sides
Name
Picture
Sum of Interior 7 8 9 10
Heptagon
Octagon
Nonagon
Decagon

6. The BASIC Polygons – Part 3
# of Sides
Name
Picture
Sum of Interior 12 n
dodecagon
n-gon

7. Sum = 180(n-2) n = the number of sides Sum of the interior
We can find the sum of the interior angles of any polygon using the formula
Sum = 180(n-2)
n = the number of sides
Back to the chart

8. The BASIC Polygons – Part 1
# of Sides
Name
Picture
Sum of Interior 3 4 5 6
Triangle
180°
Quadrilateral
360°
Pentagon
540°
Hexagon
720°

9. The BASIC Polygons – Part 2
# of Sides
Name
Picture
Sum of Interior 7 8 9 10
Heptagon
900°
Octagon
1080°
Nonagon
1260°
Decagon
1440°

10. The BASIC Polygons – Part 3
# of Sides
Name
Picture
Sum of Interior 12 n
dodecagon
1800°
n-gon
180(n-2)°

11. The algebra of Sum of the interior
Find the value of x. (4x) (2x + 9) + (3x + 8) = 540
113°
X = 33

12. More Interior Angle Stuff
The sum of the interior angles of a polygon is degrees. What is the name of the polygon?
11-gon
We’ll know tomorrow

13. Sum of the Exterior
The sum of the exterior angles of a polygon is simple … it always equals
360°

14. A single exterior angle
Find the measure of an exterior angle of a regular heptagon. Round to the nearest tenth if necessary.
51.4°

15. They are supplementary
Interior and Exterior
What is the relationship between an individual interior and exterior angle?
They are supplementary

16. More Algebra
Find the value of x. x x = 540
138°
100°
X = 64