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Download Chapter 11 – Area of Polygons and Circles Section 11.1
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Transcript
Chapter 11 – Area of Polygons and Circles Section 11.1 - Angle Measures in Polygons *Watch this video to give you a better grasp of the concepts listed below.* Polygon # of sides # of 's Sum of interior angles Triangle Quadrilateral Pentagon Hexagon Decagon n-gon Theorems about Interior Angles Thm 11.1- Polygon Interior Angles Thm. The sum of the measures of the interior angles of a convex n-gon is: Corollary to Thm 11.1 The measure of each interior angle of a regular n-gon is: Exterior angle: Theorems about Exterior Angles Thm 11.2 - Polygon Exterior Angles Thm The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°. Corollary to Thm 11.2 The measure of each exterior angle of a regular n-gon is: Example 1: A heptagon has 4 interior angles that measure 160° each and 2 interior angles that are right angles. What is the measure of the other interior angle? Example 2: The measure of each interior angle of a regular polygon is 165 . How many sides does the polygon have? Example 3: The sign has a hexagon shape. Four of the interior angles measure 140° and the remaining angles are congruent. What is the measure of the congruent angles? Example 4: Example 5: The measure of each exterior angle of a regular polygon is 40°. How many sides does the polygon have? Example 6: If you were designing a sign, would it be possible to make a sign that is a regular polygon with each interior angle measure of: a) 160° b) 115°