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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