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[6-1] Polygon Angle-Sum Theorems

This lesson focuses on finding the sum of interior angles and exterior angles of polygons. It covers equilateral, equiangular, and regular polygons. The lesson also includes jokes and homework practice.

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[6-1] Polygon Angle-Sum Theorems

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  1. [6-1] Polygon Angle-Sum Theorems Mr. Joshua Doudt Geometry (H) 12/8/2015

  2. Objective • To find the sum of the measures of interior angles of a polygon • To find the sum of the measures of exterior angles of a polygon

  3. Lesson Vocabulary • Equilateral Polygon • Equiangular Polygon • Regular Polygon

  4. Essential Understanding • The sum of the interior angle measures of a polygon depedns on the number of sides the polygon has. • By dividing a polygon with n sides into (n-2) triangles, you can show that the sum of the interior angles measure of any polygon is multiple of 180

  5. Theorem 6-1 • The sum of the measures of the interior angles of an n-gon is (n-2)180.

  6. Finding a polygon angle sum • What is the sum of the interior angle measures of a heptagon? Sum = = = =900

  7. Got it? 1a) What is the sum of the interior angle measures of 17-gon? Answer: 2700 1b) The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon? Answer: 140

  8. Polygons An equilateral polygon is a polygon with all sides congruent. An equiangular polygon is a polygon with all angles congruent A regular polygon is a polygon that is both equilateral and equiangular.

  9. Corollary to the Polygon Angle-Sum Theorem • The measure of each interior angle of a regular n-gon is

  10. Using Polygon Angle-Sum Theorem • The common housefly, Musca domestica, has eyes consists of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet?

  11. Using the Polygon Angle-Sum Theorem What is in pentagon TODAY? 110 120 150

  12. 100 30 50 105 65 81 109

  13. Theorem 6-2 • The sum of the measures of the exterior angle of a polygon, one at each vertex is 360.

  14. Finding an exterior angle measure What is in the regular octagon at the bottom?

  15. Joke Time • What kind of guns do bees use? • BeeBee guns! • How much does a pirate pay for corn? • A buccaneer! • What happened when the butcher backed into his meat grinder? • He got a little behind in his work.

  16. Homework • Pg 356 • #7-25

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