7.3 Formulas for Polygons Objectives: 1.Know and use formulas for polygons: i.sum of interior angles ii.sum of exterior angles iii.number of diagonals.

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Presentation transcript:

7.3 Formulas for Polygons Objectives: 1.Know and use formulas for polygons: i.sum of interior angles ii.sum of exterior angles iii.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°. Theorem 56: If one exterior angle is taken at each vertex, then the sum S e of the measures of the exterior angles of a polygon is given by the formula S e = 360˚. Theorem 57: The number d of diagonals that can be drawn in a polygon of n sides is given by the formula

S i = 3240°, S e = 360°, d = 170 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.

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

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

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