Interior and Exterior Angles of a Polygon Exterior Angle Interior Angle Interior Angle means inside angle Exterior Angle means outside angle To find the exterior angle extend a side outside the polygon and then rotate the arm to line up with the next side

The sum of the exterior angles As the red arm moves around the triangle it turns through the exterior angle at the end of each side. It turns through 360 o as it travels around the triangle. So the exterior angles add upto 360 o.

Similarly for this pentagon – the arm turns through 360 o as it travels around the pentagon. So for all polygons the exterior angles add up to 360 0

Regular Polygons – exterior angles If a polygon is regular then: all the exterior angles are equal The exterior angles add upto So for an equilateral triangle each exterior angle is : 120 o

90 o For all polygons the exterior angles add up to exterior angles Size of exterior angle = 5 exterior angles Size of exterior angle = 6 exterior angles Size of exterior angle = 72 o 60 o

Regular Polygons – interior angles If a polygon is regular then: all the interior angles are equal If we know the exterior angle then to find the interior subtract it from 120 o o

For all polygons the interior angles = 180 – exterior angle 4 exterior angles Size of exterior angle = 5 exterior angles Size of exterior angle = 6 exterior angles Size of exterior angle = Interior angle 180 – 90 = 90 o Interior angle 180 – 72 = 108 o Interior angle 180 – 60 = 120 o 90 o 108 o 120 o

Non Regular polygons For a regular polygon the exterior angles are all EQUAL For a non regular polygon exterior angles still add up to 360 o but they are all different.

Non Regular polygons For a regular polygon the interior angles are all EQUAL For a non regular polygon interior angles are found by: Dividing the polygon into triangles Number of sides Number of triangles Sum of interior angles 533x180 = 540 0

Number of sides Number of triangles Sum of interior angles 755x180 = 900 0

Number of sides NameNumber of triangles Sum of interior angles 4Quadrilateral Decagon Complete the chart below

Non Regular polygons Find the missing angles 160 x 90 x 80 Number of sides Number of triangles Sum of interior angles 533x180 = x + x = 540 2x = 540 X × = 540 X = ÷ 2 = 55 o