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7.3 Formulas for Polygons

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. Theorem 55 : the sum S i of the measures of the angles of a polygon with n sides is given by the formula S i = ( n – 2)180°.

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7.3 Formulas for Polygons

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  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. 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

  3. Example 1: Using the formulas, determine the sum of the measures of the interior angles, exterior angles, and the number of diagonals for an icosagon, 20-sided figure. Si = 3240°, Se= 360°, d = 170

  4. Example 2: How many sides does a polygon have if the sum of the measures’ of its interior angles is 6840°? 40 sides – a tetracontagon

  5. Example 3: How many sides does a polygon have if it has 104 diagonals? 16 sides – a hexadecagon

  6. Example 4: How many sides does a polygon have if the sum of its exterior angles is 360°? can’t tell

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