Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
6­1 Angles of Polygons
Learning Targets:
I can find and use the sum of the measures of the interior angles of a polygon
I can find and use the sum of the measures of the exterior angles of a polygon
Each cell has how many interior angles?
What comparisons can you make about each of the interior angles of each cell and generally about all of the cells?
The sum of the measures of the interior angles of a hexagon is 720. What is the measure of one interior angle of a honeycomb cell?
A reflex angle is the angle on the outside of the vertex. What would be the measure of a reflex angle of a honeycomb cell? Explain your reasoning.
Dec 30­2:19 PM
Jan 25­7:52 AM
1
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Diagonal of a polygon: a segment that connects any two nonconsecutive vertices
Diagonals can be drawn from any vertex
Notice, the diagonals cut the pentagon into three triangles
Dec 30­2:32 PM
The sum of the angle measures of a polygon is the sum of the angle measures of all the triangles formed by drawing all the possible diagonals.
Jan 22­8:16 AM
2
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Jan 22­8:16 AM
Jan 22­8:20 AM
3
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Example 1:
1. Find the sum of the measures of the interior angles of a convex nonagon.
2. Find the measure of each interior angle of parallelogram RSTU.
3. Find the sum of the measures of the interior angles of a convex octagon.
4. Find the measure of each interior angle of pentagon HJKLM.
Jan 22­8:22 AM
Jan 22­8:26 AM
4
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Example 2:
5. A mall is designed so that the five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.
6. Find the measure of each interior angle of the regular
hendecagon that appears on the face of a Susan B. Anthony one­dollar coin.
7. A certain company makes hot tubs in a variety of different shapes. Find the measure of each interior angle of the nonagon model.
Jan 22­8:28 AM
Jan 22­8:33 AM
5
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
When given one interior angle of a regular polygon, the number of sides can be found by letting the given angle be multiplied by n and setting it equal to the formula.
Example 3:
8. The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon.
9. The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.
Jan 22­8:33 AM
Now let's look at exterior angles.
Jan 22­8:37 AM
6
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Jan 22­8:39 AM
Jan 22­8:39 AM
7
Geo 6­1 Lesson with notes 1st a.notebook
January 25, 2016
Example 4:
10. Find the value of x in the diagram.
11. Find the measure of each exterior angle of a regular decagon.
Jan 22­8:41 AM
12. Find the value of x in the diagram.
13. Find the measure of each exterior angle of a regular dodecagon.
Jan 22­8:43 AM
8