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## Polygons and Angles

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**Polygons and Angles**Sec 12 -1E pg. 693 - 698**Definition**• Polygon – a simple, closed figure formed by three or more straight line segments. • A polygon is named by the letters of its vertices, written in consecutive order. Not Polygons Polygons**Polygons – or Not?**• Polygons have • Line segments are called sides • Sides meet only at their endpoints • Points of intersection are called vertices • Not Polygons • Figures have sides that cross each other • Figures are open • Figures have curved sides. Not Polygons Polygons**Regular Polygons**• An equilateral polygon has all sides congruent. • A polygon is equiangular if all of its angles are congruent. • A regular polygon is equilateral and equiangular with all sides and all angles congruent.**Number of Sides**3 4 5 6 7 8 9 10 12 n sides Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon Names of Polygons An 11 sided polygon is sometimes referred to as a undecagon or a hendecagon**Interior Angle Sum of a Polygon**• The sum of the measures of the angles of a polygon is given by • S = 180 (n – 2) • Where n represents the number of sides. The sum of the interior angles is 540 n = 5 S = 180 (n – 2) S = 180 (5 – 2) = 180 (3) S = 540**Work this problem**Find the sum of the measures of the interior angles of this polygon. This is a hexagon, so it has 6 sides. S = 180 (n – 2) What is the measure of an individual interior angle? S = 180 (6 – 2) S = 180 ( 4) The measure of an individual interior angle is 720/6 = 120 S = 720