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Published byErick Pitts Modified over 6 years ago

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Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means angles. Triangle Pentagon Octagon

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a b c e d How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

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Split the shape up into triangles

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How to find the sum of the interior angles – i.e. How to find a + b + c + d + e Split the shape up into triangles Each triangle contains 180 0 180 0

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How to find the sum of the interior angles – i.e. How to find a + b + c + d + e Split the shape up into triangles Each triangle contains 180 0 3 x 180 = 540 0 180 0

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How to find the sum of the interior angles – i.e. How to find a + b + c + d + e Split the shape up into triangles Each triangle contains 180 0 3 x 180 = 540 0 The sum of the interior angles is 540 0 180 0

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NameNumber of Sides Sum of Interior Angles Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.

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NameNumber of Sides Sum of Interior Angles Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.

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120 0 Interior Angle NB. If the polygon is regular, to find an interior angle use the rule: Int.Angle = 180 – (360 ÷ n) n is the number of sides Int. = 180 – (360 ÷ 6) 180 – 60 =120 Regular Polygons

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120 0 Interior Angle NB. If the polygon is regular, to find an exterior angle use the rule: Ext.Angle = 360 ÷ n n is the number of sides And Ext. Angle = 180 – Int.Angle Regular Polygons exterior angle (180 – 120 = 60

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