# 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.

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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

a b c e d 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

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

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

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

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.

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.

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

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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