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 Sum of interior <‘s = 3(180) = 5402 4
Sum of interior <‘s = 3(180)
= 540
Sum of 5 supplementary <‘s = 5(180)
= 900
= 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 formula d = 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