Formulas involving Polygons

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Formulas involving Polygons

• Lesson 7.3

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Sums of interior angles
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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
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Exterior angles
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5
2
4
Sum of interior lts 3(180) 540 Sum
of 5 supplementary lts 5(180)
900 900 - 540 360 Total sum of all exterior lts
360
3
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Theorem 56 If one exterior angle is taken at
each vertex, the sum Se of the measures of the
exterior lts of a polygon is given by the formula
Se 360
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Theorem 57 The number of diagonals that can be
drawn in a polygon of n sides is given by the
formulad n(n-3)
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Try draw then do the math!
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In what polygon is the sum of the measure of
exterior lts, one per vertex, equal to the sum of
the measure of the lts of the polygon?
Quadrilateral 360 360
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In what polygon is the sum of the measure of
interior lts equal to twice the sum of the measure
of the exterior lts, one per vertex?
Hexagon 720 int. 2(360) ext. 720
(n-2)(180) 720 180n 360 1080
180n n 6