Understanding Polygon Angle-Sum Theorems

Explore the Polygon Angle-Sum Theorems that determine the sum of interior angle measures in polygons. Learn about the Polygon Angle-Sum Theorem, number of sides in polygons, finding angle sums, and the corollary for regular polygons. Practice using the theorems to calculate interior angle measures in polygons like heptagons, 17-gons, and regular nonagons. Delve into real-world applications like determining angle measures in common housefly eyes with hexagonal facets. Enhance your knowledge of geometry with these theorem applications and problem-solving exercises.

• Polygon Angle-Sum Theorems
• Interior Angle Measures
• Polygons
• Geometry
• Problem-Solving

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1. 6-1 The Polygon Angle-Sum Theorems

2. Polygon Angle-Sum Theorem The sum of the measures of the interior angles of a n-gon is ? 2 180

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

4. Problem 1: Finding a Polygon Angle Sum What is the sum of the interior angle measures of a heptagon?

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

6. The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon?

10. Corollary to the Polygon Angle-Sum Theorem The measure of each interior angle of a regular n-gon is ? 2 180 ?

11. 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?

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

13. Problem 3: Using the Polygon Angle-Sum Theorem

15. 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.

16. 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

17. Problem 4: Finding an Exterior Angle Measure

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