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Formulas involving Polygons

Learn about the various formulas involving polygons, including the sum of interior angles, the sum of exterior angles, and the number of diagonals that can be drawn. Try drawing and calculating the angles yourself!

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Formulas involving Polygons

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  1. Formulas involving Polygons Lesson 7.3

  2. Sums of interior angles

  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

  4. 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

  5. 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

  6. 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!

  7. 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

  8. 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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