Download analyze #17: building a concept map

Name:
Date: September 20th, 2011
SWBAT:
POLYGONS
DEFINITIONS TO REMEMBER:
Concave polygon 
Convex polygon 
Regular polygon 
Irregular polygon 
HOW MANY DEGREES ARE IN A POLYGON? WE WILL DERIVE A FORMULA TO FIND OUT.
1. In the first row, name the polygon. In the second row, draw in as many non-intersecting
diagonals as you can. In the third row, write in the number of sides in each polygon (n). In
the last row, write the number of triangles formed:
Name
Picture
# of
sides
Triangles
n=
n=
n=
n=
n = 10
2. Reminder: how many degrees are in a triangle?
3. If each polygon below is made up of triangles, how many degrees will be in it, total? Copy
the number of sides and triangles from the table above, and then complete the last row.
Sides
Triangles
Degrees
n=
n=
n=
n=
n = 10
4. What pattern do you see in terms of the relationship between the number of sides that a
polygon has (represented by n) and the total number of degrees in it?
Formula for sum of all angles
in a polygon:
5. Refer back to your definition of a regular polygon. If we’ve found a formula for the sum of
the angles in a polygon, how could we find the measure of each angle in a regular polygon?
Formula for each angle in a
regular polygon:
6. Have some practice:
a. A polygon has 5 sides. What is the sum of all the angles of the polygon?
b. Find the sum of all the angles of a heptagon.
c. The sum of all the angles in a polygon is 1440°. What type of polygon is it?
d. If a quadrilateral is regular, find the measure of each angle.
e. Find the measure of each angle in a regular nonagon.
f. The highway department is creating new stop signs (octagons). How many degrees
should they make each angle in the stop sign?
g. On a visit to Washington DC, you go to the Pentagon,
which is the headquarters of the United States
Department of Defense. You notice that the building is
actually shaped like several pentagons inside one another,
and since you love geometry so much, decide to calculate
the sum of the building’s interior angles. What is the total
number of degrees formed by the walls of the inner
courtyard?