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Polygon Angle Theorems: Understanding Interior and Exterior Angles

Explore the Polygon Angle-Sum Theorem, understanding interior and exterior angles of polygons, and calculating angle measures. Learn about equilateral, equiangular, and regular polygons. Solve angle measure problems with different polygons using the Polygon-Angle Theorem.

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Polygon Angle Theorems: Understanding Interior and Exterior Angles

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  1. 6.1 The Polygon Angle – Sum Theorems • Theorem 6.1 – Polygon Angle-Sum Theorem • The sum of the measures of the interior angles of an n-gon is (n – 2) * 180.

  2. Finding a Polygon Angle Sum • What is the sum of the interior angle measures of a heptagon? Sum = (n – 2) * 180 = (7 – 2) * 180 = 5 * 180 = 900° The sum of the interior angle measures of a heptagon is 900°.

  3. An equilateral polygon is a polygon with all sides congruent. • An equiangular polygon is a polygon with all angles congruent. • A regular polygon is a polygon that is both equilateral and equiangular. Regular Polygon Equilateral Polygon Equiangular Polygon

  4. Corollary to the Polygon Angle-Sum Theorem • The measure of each interior angle of a regular n-gon is

  5. Using the Polygon Angle-Sum Theorem • The common housefly, Musca domestica, has eyes that consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet?

  6. Using the Polygon-Angle Theorem • What is the measure of angle Y in pentagon TODAY?

  7. Using the Polygon-Angle Theorem

  8. Polygon Exterior Angle-Sum Theorem • The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

  9. Finding an Exterior Angle Measure • What is the measure of angle 1 in the regular octagon?

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