7.3 Formulas for Polygons

1. 7.3 Formulas for Polygons • Objectives: • Know and use formulas for polygons: • sum of interior angles • sum of exterior angles • number of diagonals in a polygon

2. 7.3 worksheet 7.3

3. Theorem 55: The sum Si of the measures of the angles of a polygon with n sides is given by the formula Si = (n-2)180. Theorem 56: If one exterior angle is taken at each vertex, then the sum Se of the measures of the exterior angles of a polygon is given by the formula Se= 360°. Theorem 57: The number d of diagonals that can be drawn in a polygon of n sides is given by the formula d = n(n – 3)/2 7.3

4. Using the formulas, determine the sum of the measure of the interior angles and exterior angles, and the number of diagonals for an icosagon, 20-sided figure. Si = 3240°, Se= 360°, d = 170 7.3

5. How many sides is a polygon have if the sum of the measures’ of its interior angles is 6840°. 40 sides – a tetracontagon 7.3

6. How many sides is a polygon have if it has 104 diagonals. 16 sides – a hexadecagon 7.3

7. How many sides is a polygon if the sum of its exterior angles is 360°. can’t tell 7.3