Polygons

 Marked June 7th Home

=//Definitions//=

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 //Polygon//- a two dimensional shape formed by connecting three or more line segments at verticies. The term originates from "poly" the Greek meaning of many, and "gon" from "gonia" the meaning of a closed figure. =====

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//Convex Polygon// - a polygon with all interior angles less than 180 degrees, all diagonals drawn from any vertex remain within the polygon =====

- a polygon with parts of some line segments (diagonals) joining two verticies on the polygon outside the polygon
//Regular Polygon //- a polygon with all side lengths equal and all interior angles equal, also termed as equilateral and equiangular. (ie. square, equilateral triangle)

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There is no formula for determining the sum of a polygon's exterior angles - all regular polygon's exterior angles have a sum of 360
But for finding each of the exterior angles one can just divide the exterior angle total by the number of sides or take one angle and use supplementay angles to subtract the interior angle by 180°

180 - 150 = 30
=//Examples//= sum= 180(n-2) =180(12-2) =180(10) =1800**°**
 * a)**find the sum of the interior angles of a dodecagon (12 sided polygon)

sum= 180° 140n=180(n-2) 140n=180n-360 140n-180n=-360 -40/-40 = -360/-40 n=9
 * b)** how many sides would a polygon have all of its interior angles measured 140**° ?**

sum= 180(n-2) = 180(5-2) = 180(3) = 540**°**
 * c)**a regular polygon has 5 sides, find the measures of each interior angle.

each= 540/5 = 108**°**

=//Naming Polygons//= Triskaidecagon || 13 || 1980° || Trigon || 3 || 180° || Tetradecagon/ Tetrakaidecagon || 14 || 2160° || /Tetragon || 4 || 360° || Pentdecagon || 15 || 2340° || Ennedecagon || 19 || 3060° || Enneagon || 9 || 1260° || Icosagon || 20 || 3240° || //Angles though not truely apart of polygons is valid but is from the  //Angles section. Click on the Link to see angles after finishing this page.
 * Name || Edges || <span style="text-align: center; display: block; font-family: 'Times New Roman', Times, serif; font-size: 110%;">Interior Angles || Name || Edges || <span style="text-align: center; display: block; font-family: 'Times New Roman', Times, serif; font-size: 120%;">Interior Angles ||
 * Henagon || 1 || -360° || Dodecagon || 12 || 1800° ||
 * Digon || 2 || 0° || Tridecagon/
 * Triangle/
 * Quadrilateral
 * Pentagon || 5 || 540° || Hexdecagon || 16 || 2520° ||
 * Hexagon || 6 || 720° || Heptadecagon || 17 || 2700° ||
 * Heptagon || 7 || 900° || Octadecagon || 18 || 2880° ||
 * Octagon || 8 || 1080° || Nonadecagon/
 * <span style="font-family: 'Times New Roman', Times, serif;"> Nonagon/
 * Decagon || 10 || 1440° || Chiliagon || 1 000 || 179640° ||
 * Hendecagon || 11 || 1620° || Megagon || 1 000 000 || 179999640° ||

=//History of the Polygon//= Polygons were descovered in ancient times by the greeks. In 1796, Gause descovered the first 17 sided regular polygon when he was only 18 years old.From then, people all over the world have been finding many different types of polygons. Even historiens have found polygon shapes on ancient artifacts. The most recent discovery of polygons is on mars, scientists have found polgyon like shapes on the surface of the planet.

=<span style="font-family: Arial, Helvetica, sans-serif; color: rgb(0,0,0);"> = <span style="font-family: Arial, Helvetica, sans-serif; color: rgb(212,22,22);">//**<span style="color: rgb(0,0,0);">Works Cited: **//

<span style="color: rgb(0,0,0);">Hendriks, J., MPM 1D1, (2009). / Knill, G. ET ALL(1999). //Math Power 9//. ///Google Images//. (2009). / Knill, G. ET ALL(1993). //Math Power 9//.