1. 7.3 Formulas Involving Polygons

2. Before We Begin

3. How to name Your Polygon A polygon is named # of sides-gon Ex) A polygon with 3 sides = 3-gon A polygon with 7 sides = 7-gon

4. # of Sides or Vertices Polygon 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon # of Sides or Vertices Polygon 8Octagon 9Nonagon 10Decagon 12Dodecagon 15Pent decagon nn-gon So how do we find the sum of measures of the five angles in the figure?

5. To answer that question start at any vertex and draw diagonals.

6. Theorem 55 The sum interior angles of the measures of the angles of a polygon with n sides is given by the formula

7. Theorem 56 If one exterior angle is taken at each vertex, the sum of the measures of the exterior angles of a polygon is given by the formula

8. Theorem 57 The number d of diagonals that can be drawn in a polygon of n sides is given by the formula