6-1 The Polygon Angle-Sum Theorems - Weebly
[Pages:2]6-1 The Polygon Angle-Sum Theorems
Objective
SWBAT find the sums of the measures of the interior and exterior angles of a
polygon.
Important Info
The sum of the interior angle measures of a polygon depends on the number of
________ the polygon has.
By ___________ the polygon with n sides into ________ triangles, you can
show that the sum of the interior angle measures of any polygon is a multiple of
______.
Theorem 6-1 Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is ____________.
Example 1
Finding a Polygon Angle Sum
What is the sum of the interior angle measures of a heptagon?
What is the sum of the interior angle measures of a 17-gon?
The sum of the interior angle measures of a polygon is 1980. How can you find
the number of sides in the polygon?
Vocabulary
? An ________________________ is a polygon with all _______ congruent.
? An ________________________ is a polygon with all _______ congruent.
? An ________________________ is a polygon that is __________.
Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a _____________ n-gon is __________
Example 2 Using the Polygon Angle-Sum Theorem
The common housefly has eyes that consist of approximately 4,000 facets. Each
facet is a regular hexagon. What is the measure off each interior angle in one
hexagonal facet?
What is the measure of each interior angle in a regular nonagon?
T
110
Example 3
Using the Polygon Angle-Sum Theorem
Y
What is m ................
................
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