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## Formulas involving Polygons

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**Formulas involving Polygons**Lesson 7.3**Theorem 55: Sum Si of the measure of the angles of a**polygon with n sides is given by the formula Si = (n-2)180**Exterior angles**1 5 2 4 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 3**Theorem 56 : If one exterior angle is taken at each vertex,**the sum Se of the measures of the exterior <‘s of a polygon is given by the formula Se = 360**Theorem 57: The number of diagonals that can be drawn in a**polygon of n sides is given by the formulad = n(n-3) 2 Try: draw then do the math!**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**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