Geo Notes 6-1
Name:
Essential Question 1. ________________________________________________________________________________________________
_________________________________________________________________________________________________________________________
Answer _______________________________________________________________________________________________________________
_________________________________________________________________________________________________________________________
New Vocab: 1._____________, 2._____________, 3._____________,
4.________________________
Theorem 6-1: Polygon Angle-Sum Theorem
The _______________ of the measures of the ________________________________ of a _______________ is __________________.
Problem 1: Finding a Polygon Angle Sum.
A. What is the sum of the
interior angles of a
heptagon?
Equilateral polygon
B. What is the sum of the
interior angles of a 17-gon?
C. The sum of the measures of the interior angles of a
polygon is 1980. How can you find the number of sides
in the polygon?
Equiangular polygon
Regular polygon
Corollary to the Polygon Angle-Sum Theorem
The measure of each ______________________ of a ____________________ is _____________________________
Problem 2: Using the Polygon Angle-Sum Theorem
Biology ~ The common housefly, has eyes that consist of approximately 4000 facets. Each facet is a
regular hexagon. What is the measure of each interior angle of one hexagonal factet?
2B. What is the measure of each interior angle in a regular nonagon?
Problem 3: Using the Polygon Angle-Sum Theorem
A.
Find m∠𝑌
B.
Find m∠𝐺
Theorem 6-2: Polygon Exterior Angle-Sum Theorem
The ____________ of the measures of the ________________________________________ of any polygon is ________________.
In any _____________________ polygon each __________________ and __________________ will equal ____________
Problem 4: Finding an Exterior Angle Measure
A.
What is m∠𝑌 in the regular octagon?
B.
What is the measure of an exterior angle of a
regular nonagon?
5. 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.
A. 72
B. 30