Happy Monday!
• Take out your worksheet from Friday
• Take out your whiteboard marker and whiteboard
• Take out a piece of paper and title it
– 6.1: Angles of Polygons
• Pick up the paper from the front table
Homework: p 386 #1-15, 23-33 odd
3 Things
Lets’ Warm-Up!
1) Sketch a polygon on your whiteboard.
Compare with someone Horizontal to you. Do you
agree it’s a polygon?
2) Sketch a non-example of a polygon on your
whiteboard.
Compare with someone Vertical to you. Do you
agree it is not a polygon?
Lets’ Warm-Up!
3) With the person vertical to you discuss the
difference between a concave and convex polygon.
Sketch a concave and convex polygon on your
whiteboard.
4) With the person horizontal to you, discuss the
difference between a regular and irregular polygon.
Sketch a regular and irregular polygon on your
whiteboard.
Whiteboard
1. Tell whether the figure is a polygon.
If it is a polygon do the following:
o name it by the number of sides
o Decide whether it is regular or irregular
o Decide whether it is concave or convex
(a)
(d)
6.1: Angles of Polygons
• Learning Objective
– SWBAT find and use the measures of interior and
exterior angles of polygons
Vertex
• Common endpoint of two sides.
Diagonal
• A segment that connects any two nonconsecutive
vertices.
Whiteboards
• How many degrees do a triangle add up to?
Interior Angles of a Convex Polygon
1. Draw a convex polygon.
2. Draw all possible diagonals from one vertex
of the polygon
3. How many triangles did you create?
1. How many degrees do you think the interior
angles of your polygon add up to?
Ex)
6-1 Properties and Attributes of Polygons
Deriving the Polygon Angle Sum Theorem
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
Number of Sides
Number of Triangles
that can create the
polygon
Sum of Interior
Angle Measures of
the polygon
Formula..
• Talk with your partner…
Can you come up with a formula to determine
the sum of the interior angles measures of a
convex polygon with n sides?
Polygon Angle Sum Theorem
Example 1: Finding the Interior Angle
Measures and Sums in Polygons
Find the sum of the interior angle measures of a
convex heptagon.
Whiteboards
Find the measure of each interior angle of a
regular 16-gon.
Whiteboards
• Find the measure of <C
Exterior Angles
Whiteboards:
Looking at the same figure from the last problem, draw
one exterior angle on the polygon.
If I am to continue drawing exterior angles for every side
of my polygon, I must continue in the same direction. For
example if I began clockwise, I must continue clockwise.
Exterior Angles
Exterior Angle
• An exterior angle is formed by one side of a
polygon and the extension of a consecutive
side
6-1 Properties and Attributes of Polygons
Exploring Polygon Exterior Angle Sum Theorem
On the back of your worksheet, attempt to use the two
examples of polygons with exterior angles to understand what
the sum of all exteriors angles of any polygon will be.
http://www.mathopenref.com/polygonexteriorangles.html
Polygon Exterior Angle Sum Theorem
o The Sum of exterior angle measures of a convex polygon is
360°.
Exterior Angles
Here are polygons with their exterior angles.
What do they both have in common?
Exterior Angles
• The sum of the exterior angle measures (one
angle at each vertex) of a convex polygon is
360°
• OR
• 360/ n= each exterior angle
Example 2: Finding Exterior Angle
Measures in Polygons
Find the measure of each exterior angle of a
regular 20-gon.
Whiteboards
Find the value of b in polygon FGHJKL.
Whiteboards
• Find the measure of each exterior angle of a
regular dodecagon.
Example 3: Application
Ann is making paper stars for party
decorations. What is the measure of 1?
Whiteboards
The aperture of the camera is
formed by 8 blades. What
would the measure of each
exterior angle be?
What if…?
It was 10 blades instead of 8?
Exit Ticket
1. Name the polygon by the number of its sides.
Then tell whether the polygon is regular or
irregular, concave or convex.
1. Find the sum of the interior angle measures of a
convex 11-gon.
2. Find the measure of each interior angle of a
regular 18-gon.
3. Find the measure of each exterior angle of a
regular 15-gon
Think – Write - Share
Answer the following question on your worksheet
under Todays Summary.
How would you summarize todays lesson for
someone who wasn’t here?