# LESSON PLAN #1: Discover a Relationship

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4 Name Polygons What is a polygon? Remember the sum of the interior angles of a triangle Let s investigate the sum of the angles of the following polygons: Polygon Drawing # of sides # of triangles sum of interior sum of exterior Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon DoDecagon n-gon Hypothesis: 1) What can you say about the sum of the interior angles of a polygon (related to the number of sides n)? 2) What happens if we divide that result by the number of sides (n)?

5 Practice: 1)What is the sum of the angles in a decagon? 2)What is the sum of the angles in a heptagon? o 3)What is the name of the polygon whose interior angles sum to 5760? Find the sum of the measures of the interior angles of a regular polygon with the given number of sides: 4) 9 5) 11 6) 10 7) 18 For a regular polygon with the given number of sides, find the sum of the measures of the exterior angles: 8) 15 9) 40 10) 22 11) 100 Find the measure of one interior angle of a regular polygon with the given number of sides: 12) pentagon 13) dodecagon 14) octagon 15) heptagon 16) 20 sided 17) 24-sided 18) What is the name of the figure whose interior angles all equal 150 0? Find the number of sides of a polygon whose interior angles have the given number as the sum of their measures: 19) ) ) )

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