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# Download 6. 8. exterior ∠ sum = sum of supplementary∠`s – interior ∠ sum

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Exterior Angles GEOMETRY NAME_________________________ DATE __________ Per.___________ Polygons that each interior/exterior angle pair 6. Note of a polygon is supplementary. interior ∠ regular polygon # of ∠ ‘s exterior ∠ measure triangle 3 square pentagon hexagon octagon decagon exterior ∠ Use that information to calculate the exterior angle measures and sums of each regular polygon in the table at right. a) Use the table in #6 to graph the exterior angle sums of an n-sided regular polygon. 7. e x t e r i o r 900° 720° 540° 360° 180° S u m 0° 1 2 3 4 5 6 7 8 9 10 3(120°)=360° 4( )= Use the table in #6 to graph the exterior angle 8. a) measures of an n-sided regular polygon. y E x t e r i o r 180 - 60 = 120° exterior ∠ sum x ∠ y 120° 100° 80° 60° 40° 20° 0° 1 # of sides of a regular n-sided polygon 2 3 4 5 6 7 8 9 10 x # of sides of a regular n-sided polygon b) Are the graphed points collinear? c) What does the graph imply for n = 7 & 9? b) Are the graphed points collinear? d) Find an equation for the line through the pts.: c) Is each quotient an exterior angle measure? 360÷3 = 360÷4 = 360÷5 = e) Does this graph verify your guess in #5? f) Should these plotted points be connected? Why not? 9. 360÷6 = 360÷8 = 360÷10 = d) Find a equation for the curve through the pts.: (HINT: See part c) Recall that adjacent interior/exterior angles are linear pairs. So, in a polygon with n-sides, there are also ____ vertices. Hence, there are also n pairs of _____________ angles. The sum of all of the polygon’s supplementary angles is______, which is the sum of the interior and exterior ∠’s. Substitute the formulas below to derive the exterior angle sum of any convex polygon. exterior ∠ sum = sum of supplementary∠’s – interior ∠ sum formula ( ) – ______( ___ – ___ ) exterior ∠ sum= = = 10. Show that: 180 − 180(n − 2) 360 = n n