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7.4 Regular Polygons

7.4 Regular Polygons. Objectives: Recognize regular polygons Use a formula to find the measure of an exterior angle of an equiangular polygon. Polygons that are both equilateral and equiangular are regular. Formula you know: Sum of the exterior angles of a polygon = 360°

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7.4 Regular Polygons

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  1. 7.4 Regular Polygons • Objectives: • Recognize regular polygons • Use a formula to find the measure of an exterior angle of an equiangular polygon.

  2. Polygons that are both equilateral and equiangular are regular.

  3. Formula you know: Sum of the exterior angles of a polygon = 360° Theorem 58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula:

  4. Formula you know: Sum of all interior angles of a polygon = (n – 2)180° The measure of EACH interior angle of a regular polygon is found by the formula:

  5. Example 1: Find the measure of each exterior angle of a regular octagon.

  6. Example 2: If each angle of a polygon measures 108°, find the number of sides.

  7. Example 3: What is the name of the polygon if each exterior angle measures 60°?

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