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**6-1 The Polygon Angle-Sum Theorems**

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**Polygon Angle-Sum Theorem**

The sum of the measures of the interior angles of a n-gon is 𝑛−2 180

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NUMBER OF SIDES NAME 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon

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**Problem 1: Finding a Polygon Angle Sum**

What is the sum of the interior angle measures of a heptagon?

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**What is the sum of the interior angle measures of a 17-gon?**

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**The sum of the interior angle measures of a polygon is 1980**

The sum of the interior angle measures of a polygon is How can you find the number of sides in the polygon?

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**Corollary to the Polygon Angle-Sum Theorem**

The measure of each interior angle of a regular n-gon is 𝑛−2 180 𝑛

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**Problem 2: Using the Polygon Angle-Sum Theorem**

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 in on hexagonal facet?

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**What is the measure of each interior angle in a regular nonagon?**

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**Problem 3: Using the Polygon Angle-Sum Theorem**

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**You can draw exterior angles at any vertex of a polygon**

You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of the exterior angles, one at each vertex is 360.

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**Polygon Exterior Angle-Sum Theorem**

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For the pentagon

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**Problem 4: Finding an Exterior Angle Measure**

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**What is the measure of an exterior angle of a regular nonagon?**

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