m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Polygon: A closed figure with three or more sides is called a polygon. The sum (S) of the measures of the interior angles of a polygon is given by: S=180(n2) n = # of sides Example: A decagon is a 10 sided polygon. What is the sum of all of the interior angles in a decagon? Ex: Determine the missing measure in the figure shown. 135° 80° 100° 65° x 1 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Ex: Determine the missing measure: 135° 150° x° 80° 125° 135° 130° Sometimes we have the find the number of sides (n) given the sum (S) Ex: Determine the number of sides of a polygon whose interior angles add up to 1980° 2 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Regular and Irregular polygons When all sides are equal, it is called a regular polygon. A polygon where all sides are not equal is called irregular. Examples of regular polygons: In regular polygons, all interior angles are equal. 3 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 To find the measure of EACH interior angle in a regular polygon, Each interior angle in a regular polygon = S , where S = sum, n = # of n sides Example: For Superhero Day, Ms. MacDonald has designed a crest for her costume. The hexagon in the crest is regular. Determine the measure of each angle in the hexagon. 4 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Example: Determine the measure of each interior angle in a regular pentadecagon (15 sided polygon). Sometimes, we have to find n (# of sides) given the interior angle Each interior angle = Example: The measure of each interior angle in a regular polygon is 144°. How many sides does the polygon have? 5 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Example: Determine the number of sides in a regular polygon where the interior angle is 135°. Example: Find the measure of w, x. y and z. z w y x 6 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 Find x: 120° A) x B) 88° 110° x° 110° 120° 128° 120° 135° 82° 36° D) C) 84° (8x30)° 105° 120° (4x+40)° (6x+10)° x 121° (3x+10)° Page 99 # 1, 2, 3, 6, 7a, 10, 11, 16 7 m2201 chapter 2 section 2.4 polygons 2013.notebook October 28, 2013 8

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