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Understanding Regular Polygons: Exterior Angles and Their Measures

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This lesson focuses on recognizing regular polygons and using formulas to calculate the measure of their exterior angles. Regular polygons are defined as those that are both equilateral and equiangular. The sum of the exterior angles of any polygon is always 360°. For equiangular polygons with n sides, the measure of each exterior angle can be calculated using specific formulas. The lesson includes examples that demonstrate these concepts, such as finding exterior angles of a regular octagon and determining polygon types based on angle measures.

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Understanding Regular Polygons: Exterior Angles and Their Measures

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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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