 # Objective: To be able to work out the interior and exterior angles of a polygon.

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Objective: To be able to work out the interior and exterior angles of a polygon

What is a polygon? They are flat and closed A polygon is a 2D shape that is made up of straight lines

180 o What do the angles inside a triangle always add up to? These are interior angles – they are on the inside

180 o What do the interior angles of a quadrilateral always add up to? 180 o + 180 o = 360 o

Pentagon 180 o 3 x 180 o = 540 o

Hexagon 180 o 4 x 180 o = 720 o

Heptagon 180 o 5 x 180 o = 900 o

Octagon 180 o 6 x 180 o = 1080 o

Name of polygon Number of sides Number of triangles inside polygon Sum of interior angles Triangle311 x 180 =180 o Quadrilateral422 x 180 =360 o Pentagon Hexagon Heptagon Octagon A polygon with n sides 5 6 7 8 n 3 4 5 6 n - 2 3 x 180 = 4 x 180 = 5 x 180 = 6 x 180 = (n-2) x 180 = 540 o 720 o 900 o 1080 o 180(n – 2) o

IMPORTANT If a polygon has n sides, we can split it up into n triangles So the sum of the interior angles of the n-sided polygon is 180(n – 2) o

Exterior Angles EXTERIOR ANGLES ALWAYS ADD TO 360 o These are exterior angles – they are on the outside

Angles in Parallel Lines These always add to make 180 o

Summary  A polygon is a flat shape made from straight lines  The external angles of a polygon always add to 360 o  The internal angles of an n-sided polygon add to 180(n – 2) o

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