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## Polygons

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**Polygons**The word ‘polygon’ is a Greek word. Poly means many and gon means angles.**Examples of Polygons**Polygons**These are not Polygons**Polygons**Terminology**Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Polygons**Vertex**Side Polygons**Interior angle: An angle formed by two adjacent sides**inside the polygon. • Exterior angle: An angle formed by two adjacent sides outside the polygon. Polygons**Exterior angle**Interior angle Polygons**Let us recapitulate**Exterior angle Vertex Side Diagonal Interior angle Polygons**Types of Polygons**• Equiangular Polygon: a polygon in which all of the angles are equal • Equilateral Polygon: a polygon in which all of the sides are the same length Polygons**Regular Polygon: a polygon where all the angles are equal**and all of the sides are the same length. They are both equilateral and equiangular Polygons**Examples of Regular Polygons**Polygons**A convex polygon: A polygon whose each of the interior angle**measures less than 180°. If one or more than one angle in a polygon measures more than 180° then it is known as concave polygon. (Think: concave has a "cave" in it) Polygons**IN TERIOR ANGLES OF A POLYGON**Polygons**Let us find the connection between the number of sides,**number of diagonals and the number of triangles of a polygon. Polygons**180o**180o 180o 180o 2 1 diagonal 3 x 180o = 540o 180o 5 180o 180o 180o 180o 180o 4 sides Quadrilateral 5 sides Pentagon 2 x 180o = 360o 3 2 diagonals 180o 180o 180o 180o 6 sides Hexagon Heptagon/Septagon 7 sides 4 x 180o = 720o 4 5 x 180o = 900o 3 diagonals 4 diagonals Polygons**1**Calculate the Sum of Interior Angles and each interior angle of each of these regular polygons. 7 sides Septagon/Heptagon Sum of Int. Angles 900o Interior Angle 128.6o 2 3 4 9 sides 10 sides 11 sides Nonagon Decagon Hendecagon Sum 1260o I.A. 140o Sum 1440o I.A. 144o Sum 1620o I.A. 147.3o Polygons**x**75o 100o 95o w 115o 110o 75o 70o 125o 125o z 138o 100o 140o 105o 121o 138o 117o 133o y 137o Diagrams not drawn accurately. Find the unknown angles below. 2 x 180o = 360o 3 x 180o = 540o 360 – 245 = 115o 540 – 395 = 145o 4 x 180o = 720o 5 x 180o = 900o 720 – 603 = 117o 900 – 776 = 124o Polygons**EXTERIOR ANGLES OF A POLYGON**Polygons**B**A C F 1 2 E D Y An exterior angle of a regular polygon is formed by extending one side of the polygon. Angle CDY is an exterior angle to angle CDE Exterior Angle + Interior Angle of a regular polygon =1800 Polygons**1200**600 1200 600 600 1200 Polygons**1200**1200 1200 Polygons**1200**1200 1200 Polygons**3600**Polygons**600**600 600 600 600 600 Polygons**600**600 600 600 600 600 Polygons**3**4 2 5 1 6 600 600 600 600 600 600 Polygons**3**4 600 600 2 600 600 5 600 600 1 6 Polygons**3**4 2 3600 5 1 6 Polygons**900**900 900 900 Polygons**900**900 900 900 Polygons**900**900 900 900 Polygons**2**3 3600 1 4 Polygons**No matter what type of polygon we have, the sum of the**exterior angles is ALWAYS equal to 360º. Sum of exterior angles = 360º Polygons**In a regular polygon with ‘n’ sides**Sum of interior angles = (n -2) x 1800 i.e. 2(n – 2) x right angles Exterior Angle + Interior Angle =1800 Each exterior angle = 3600/n No. of sides = 3600/exterior angle Polygons**Let us explore few more problems**• Find the measure of each interior angle of a polygon with 9 sides. • Ans : 1400 • Find the measure of each exterior angle of a regular decagon. • Ans : 360 • How many sides are there in a regular polygon if each interior angle measures 1650? • Ans : 24 sides • Is it possible to have a regular polygon with an exterior angle equal to 400 ? • Ans : Yes Polygons**Thank You**Polygons DG