06+Polygons+and+Angle+Measures+in+Polygons


 * Polygons and Angle Measures in Polygons**


 * Polygon:** a closed plane figure bounded by straight sides

Convex Polygons & Concave Polygons:   **A polygon with 6 sides contains 4 triangles. Therefore, the equation for the interior angle measures is the number of sides, minus two, times 180.
 * Polygon Interior Angles Theorem:** the sum of the measures of the interior angles of a convex n-gon is **// (n-2)180˚ //**

 **Polygon Exterior Angle Theorem: **The sum of the measures of the exterior angles of a convex polygon is 360˚. the measure of each exterior angle of s regular n-gon is 360˚/n.

http://www.mathleague.com/help/geometry/polygons.htm#polygon @http://www.mathsisfun.com/geometry/polygons.html**


 * Example Problems:**

1.) A convex hexagon has angles that measure 60, 132, 130, 145, and 80. What is the measure of the sixth interior angle? (n-2)180 (6-2)180 (4)180 720˚

60 + 132 + 13 + 145 +80 = 547 720 - 547 = 173˚

A Convex 14-gon has 14 sides. What is the interior angle sum?

(n-2)18, (14-2)180 (12)180 2160

What is the exterior angle sum of any regular polygon?

360 degrees

A Convex Hexagon has 6 sides. What is the measure of one exterior angle?

360/n 360/6 60 degrees

A Convex, regular figure has interior angle measures of 144 degrees. How many sides does the figure have 144-interior 36-exterior 360/36= 10 sides A Convex, regular figue has exterior angle measures of 24 degress. What is the interior angle sum?

360/24= 15 sides 180-24= 156 156(15)= 2340 degrees