Download Angle Relationships in Polygons Investigation I

Angle Relationships in Polygons
Investigation I – 1D 5.3.1 - Polygons
1. Work with each polygon in turn starting with the Pentagon (5 sides) and fill in the table
at the bottom of this sheet. *No angles greater than 180 degrees!
2. For the 8-sided polygon, move the vertices and list your interior angles below:
S=
T=
U=
V=
W=
X=
Y=
Z=
Sum of interior angles:
3. Determine the corresponding exterior angle for each interior angle above. Use the
information you already know about interior and exterior angles.
SE =
TE =
UE =
VE =
WE =
XE =
YE =
ZE =
Sum of exterior angles:
Number of
Sides
Name
3
Triangle
4
Quadrilateral
5
6
7
8
9
10
n
Sum of
Interior Angles
Sum of
Exterior Angles
4. Manipulate each polygon until you have turned each one into a rectangle, or as close as
you can get to a rectangle. You should only have 90 degree angles and 180 degree
angles. Complete the table below.
Number of Sides
5
6
7
8
Number of 90o Angles
Number of 180o Angles
5. Explain what this table tells you about the sum of the interior angles of a polygon.
6. Determine the sum of the interior angles in a 20-sided polygon. Explain how you found
your answer.
7. Explain how to determine the sum of the interior angles in an n-sided polygon
(any polygon).
8. If you were given the sum of the interior angles in a polygon, explain how you could
determine the number of sides that polygon has.
Investigation II – 1D 5.3.2 – Regular Polygons
1. Each polygon in this demo is regular. Manipulate each regular polygon.
2. What is a regular polygon?
3. What is the measure of each angle in a regular
a. Heptagon (7 sides)
b. Octagon (8 sides)
c. 12-gon (12 sides)
4. The sum of the interior angles of a regular polygons is 7,380 degrees. What is the measure of
each interior angle? Show / explain your work!
5. A regular polygon has 55 sides. What is the measure of each interior angle?
Show / explain your work!