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Section 6.1 Notes – Geometry
The Polygon Angle-Sum Theorems
Name: _____________________________
Period: ________
Goal: Be able to find the sum of the measures of the interior and exterior angles of a polygon.
In each polygon, draw all the diagonals from one vertex. Notice that this divides each polygon into
triangular regions.
Complete the table below. What is the pattern in the sum of the measures of the interior angles of any
convex n-gon?
Polygon
Number of Sides
Triangle
3
Number of
Triangles
1
Sum of measures of
interior angles
1 • 180° = 180°
Quadrilateral
2• 180° = 360°
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
Pentadecagon
:
:
n-gon
n
:
:
___________________________
Directions: Find the SUM of the interior angle measures of each polygon.
1. Octagon
2. 36 - gon
____________________
____________________
_____________
Directions: Find the measure of ONE INTERIOR ANGLE in each regular polygon. Round to the
nearest tenth if necessary.
3.
4. Regular 18 – gon
Directions: Find the missing angle measures.
5.
Directions: The sum of the interior angle measures of a polygon with n sides is given. Find n.
6. 900
7. 215,640
In any polygon, the interior and exterior angles must be: ________________
Directions: Grab your calculators!!! Find the SUM of the exterior angles of the polygons below.
a. ______________
b. ______________
c. ______________
d. ______________
e. ______________
f. ______________
________
Directions: Find the measure of AN EXTERIOR angle of each regular polygon. Round to the nearest
tenth if necessary.
8. heptagon
9. decagon
Directions: Find the values of the variables for each regular polygon.
10.
11.
Directions: The measure of an exterior angle of a regular polygon is given. Find the measure of an
interior angle. Then find the number of sides.
12. 18
13. 12
Challenge: The measure of an interior angle of a regular polygon is four times the measure of an
exterior angle of the same polygon. What is the name of the polygon?
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