1. Aim 6.4: To explore the exterior angles of a polygon
Do Now: 1. Find the missing angles of the isosceles trapezoid provided below:
2. Solve for x:
Homework: Packet page 10
500 x 20 22

2. Aim 6.4: To explore the exterior angles of a polygon
Homework Answers:
Packet page 9
1. a) x = 2
b) AC = 10 & BD = 10
2. a) x = 20
b) PQ = 24
c) All sides are 24 so the shape is a rhombus
3. Angle BCD = 80
4. x = 6
5. x = 24
Aim 6.4: To explore the exterior angles of a polygon

3. Aim 6.4: To explore the exterior angles of a polygon
What is a Polygon?
A Polygon is a closed figure with three or more sides.
A regular polygon is a polygon that is both equilateral and equiangular.
Aim 6.4: To explore the exterior angles of a polygon

4. Number of Triangles in a Polygon
Number of Triangles in a Polygon = Number of sides - 2
Aim 6.4: To explore the exterior angles of a polygon

5. Sum of the Interior Angles of a Polygon
Formula: Sum = 180 (n – 2)
n represents the number of sides
*Think of it as the 180o times the number of triangles 1 3 2
Aim 6.4: To explore the exterior angles of a polygon

6. Aim 6.4: To explore the exterior angles of a polygon
Examples:
Example #1:
Determine the sum of the interior angles of an octagon.
Example #2:
How many sides does a polygon have if the sum of its interior angles is 720°?
Aim 6.4: To explore the exterior angles of a polygon

7. Measure of Each Interior Angle of a Regular Polygon:
Formula: Sum = 180 (n – 2) n
This formula can ONLY be used if the Polygon is regular
Aim 6.4: To explore the exterior angles of a polygon

8. What is an Exterior Angle?
An exterior angle of a polygon is an angle that is formed by extending the sides of a polygon.
Aim 6.4: To explore the exterior angles of a polygon

9. Exterior Angles of a Polygon
All polygons have an exterior angle sum of 360o
Exterior angle = 360 n
n represents the number of sides
This formula can ONLY be used if the Polygon is regular
Aim 6.4: To explore the exterior angles of a polygon

10. Aim 6.4: To explore the exterior angles of a polygon
Example #1:
Find the sum of the interior angles of a hexagon (six sides) equals:
Aim 6.4: To explore the exterior angles of a polygon

11. Aim 6.4: To explore the exterior angles of a polygon
Example #2:
How many degrees are there in each interior angle of a hexagon?
Aim 6.4: To explore the exterior angles of a polygon

12. Aim 6.4: To explore the exterior angles of a polygon
Example #3:
How many sides does a polygon have if the sum of its interior angles is 2160° ?
Aim 6.4: To explore the exterior angles of a polygon

13. Aim 6.4: To explore the exterior angles of a polygon
Example #4:
Each interior angle of a regular polygon measures 162°. How many sides does the polygon have?
Aim 6.4: To explore the exterior angles of a polygon

14. Aim 6.4: To explore the exterior angles of a polygon
Example #5:
Find the number of degrees in each exterior angle of a regular pentagon:
Aim 6.4: To explore the exterior angles of a polygon

15. Aim 6.4: To explore the exterior angles of a polygon
Example #6:
What is the sum of the exterior angles of a polygon with 36 sides?
Aim 6.4: To explore the exterior angles of a polygon

16. Aim 6.4: To explore the exterior angles of a polygon
Exit Ticket:
True or False: In a regular polygon, all sides and angles are congruent.
The formula for the measure of each interior angle is
Exterior angle = 360 n
Determine the sum of the interior angles of a 30 sided figure:
Aim 6.4: To explore the exterior angles of a polygon