1. Problem:
What is the degree measure of each interior angle and exterior angle in a regular 18-gon? 18-gon: polygon with 18 sides regular: all angles are equal all sides are equal

2. Process:
Need to know formula/pattern for total angle measures INSIDE polygons.
Need to know formula/pattern for total angle measures OUTSIDE polygons
Need to divide the total by 18

3. What I already know: The total number of degrees in a 3-sided polygon (triangle) is 180 Linear pair = 180°

4. Tips (Interior Angle Groups)
Divide the polygon into triangles and cut them out
Knowing what you already know about the angles in a triangle, determine the sum of the angles in the pentagon
Look for a patter or formula

5. Tips (Exterior Angle Groups)
Determine the sum of the INTERIOR angles first

6. 1. I think the total number of degrees INSIDE/OUTSIDE a pentagon is:
2. I think the rule for any polygon is:
3. Using this the rule the measure of each INTERIOR/EXTERIOR angle in an 18-gon is:

7. Polygons

8. Define vocabulary need to discuss polygons; find formulas for the sum of the interior and exterior angles in any polygon and use them to find angle measures in regular polygons
How is the sum of the interior angles of a polygon determined?
What is true about the sum of the exterior angles of any polygon?

9. Polygons
Closed figures
No curves
Sides meet end point to end point

11. Diagonal: a segment connecting two vertices in a polygon.

12. Types of Polygons Concave: diagonals can go outside the polygon
Convex:

13. Equiangular Polygon Equilateral Polygon
all angles are equal all sides are equal
Regular Polygon
all sides & angles are equal in measure.

14. Names of Polygons Triangle: 3 sides Octagon: 8 sides
Quadrilateral: 4 sides
Nonagon: 9 sides
Pentagon: 5 sides
Decagon: 10 sides
Hexagon: 6 sides
Undecagon: 11 sides
Heptagon: 7 sides
Dodecagon: 12 sides

15. Theorems Total of Interior Angles: 180n – 360
Total of Exterior Angles = 360°
# of sides

16. Practice Find the total sum of the interior angles in a… 1. Octagon
2. Heptagon

17. Practice Find the measure of each angle in a REGULAR 3. Nonagon
4. Decagon

18. Practice
Find the missing angle in each figure