1. Bell Work
Find x Find x and y

2. Polygons
Day 1 – Interior Angles

3. This is a chart 3 4 5 6 7 8 n 1 2 3 4 5 6 n -2 Polygon # of Sides
# of Triangles
Sum of the Angle Measures
Interior Angle Measures
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
N-gon 3 4 5 6 7 8 n 1 2 3 4 5 6
n -2

4. Example 1
Ryan’s parents are building him a sandbox to play in. It is the shape of a hexagon as shown. What is the sum of the measures of the interior angles of the hexagon?
𝑆=180(𝑛−2)
𝑆=180(6−2)
𝑆=180 4 =720

5. Example 2
The sum of the angles inside a polygon is 2340 degrees. Find the number of sides on this polygon.

6. Example 3
Find the value of x.

7. Example 4
Find the value of x.

8. Regular (Defn) Definition: Can you name a regular quadrilateral?
A regular triangle?

9. How do we find interior angles?
Polygon
# of Sides
# of Triangles
Sum of the Angle Measures
Interior Angle Measures
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
N-gon 3 4 5 6 7 8 n 1 2 3 4 5 6
n-2
180
360
540
720
900
1080
180(n-2)

10. Example 5
A regular polygon with each interior angle is 140 degrees. How many sides does the polygon have?

11. HOMEWORK
6.1 Pg 320 #’s 1-3, 7-9, 13-15, 19-20

12. Bell Work
A mall is designed so that 5 walkways meet at a food court that is in the shape of a regular pentagon. Find the sum of the measures of the interior angles of the pentagon.
A polygon that has 53 sides has how many degrees in all of their interior angles?

13. Polygons
Day 2 – Exterior Angles

14. Sum of Exterior Angles
An exterior angle is formed when one side at a vertex of a polygon is extended.
The sum of ALL the exterior angles is 360°. FOR EVERY POLYGON!!!
This is because the angles rotate around to make one revolution. (circle-has 360 degrees)

15. Example 1
Find the sum of the exterior angles and the measure of each exterior angle of a…
1. quadrilateral
gon
3. nonagon

16. Example 2 𝐸= 360 𝑛 A hexagon has an exterior angle that measures…
The formula for each exterior angle is:
𝐸= 360 𝑛

17. Example 3
A polygon has an exterior angle of 18 degrees. How many sides does the polygon have?

18. Example 4
Find the interior and exterior angle measure of a dodecagon

19. Challenge
The ratio for an exterior angle to an interior angle is 1:3. How many sides are in the shape.

20. Homework
6.1 Pg 321 #’s 10, 16, 17, 23-26, 31