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Published byClement Porter Modified over 8 years ago
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Warm Up
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7.3 Formulas involving Polygons Use important formulas that apply to polygons
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Sums of interior angles Name# of sides # of triangles Work Total degrees Triangle311 (180)180 Quadrilateral422(180)360 Pentagon533(180)540 Hexagon644(180)720 Heptagon755(180)900 Octagon866(180)1080 n-gonnn-2(n-2)(180)
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T 55: Sum S i of the measure of the angles of a polygon with n sides is given by the formula S i = (n-2)180
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Exterior angles Sum of interior <‘s = 3(180) = 540 Sum of 5 supplementary <‘s = 5(180) = 900 900 - 540 = 360 Total sum of all exterior <‘s = 360 1 2 3 4 5
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T 56 : If one exterior angle is taken at each vertex, the sum S e of the measures of the exterior <‘s of a polygon is given by the formula S e = 360
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T 57: The number of diagonals that can be drawn in a polygon of n sides is given by the formula d = n(n-3) 2 Try: draw then do the math!
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In what polygon is the sum of the measure of exterior <‘s, one per vertex, equal to the sum of the measure of the <‘s of the polygon? Quadrilateral 360 = 360
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In what polygon is the sum of the measure of interior <‘s equal to twice the sum of the measure of the exterior <‘s, one per vertex? In what polygon is the sum of the measure of interior <‘s equal to twice the sum of the measure of the exterior <‘s, one per vertex? Hexagon: 720 int. = 2(360) ext. 720 = (n-2)(180) 720 = 180n – 360 1080 = 180n n = 6
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