[6-1] Polygon Angle-Sum Theorems

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Presentation transcript:

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

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

Lesson Vocabulary Equilateral Polygon Equiangular Polygon Regular Polygon

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

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

Finding a polygon angle sum What is the sum of the interior angle measures of a heptagon? Sum = 𝑛−2 180 = 7−2 180 =5∗180 =900

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

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.

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

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?

Using the Polygon Angle-Sum Theorem What is 𝑚∠𝑌 in pentagon TODAY? 110 120 150

100 30 50 105 65 81 109

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

Finding an exterior angle measure What is 𝑚∠𝑔 in the regular octagon at the bottom? 𝑚∠1= 360 8 𝑚∠1=45

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.

Homework Pg 356 #7-25