ANGLES IN A POLYGON A polygon is any plane shape with straight lines. Examples are; Triangle 3sides 1 Quadrilateral 4sides 2triangles Pentagon 5sides 3triangles Hexagon 6sides 4triangles Heptagon 7sides 5triangles Octagon 8sides 6triangles Nonagon 9sides 7triangles Decagon 10sides 8triangles A regular polygon has all sides and all angles equal. Formula for polygon The sum of the angles of a polygon = (n – 2) x 180 or (2n – 4) x 90 or 0= (n – 2) x 2right angles or 2n – 4right angles The interior angle of a polygon = 0 (n - 2) x 180 Number of triangles in a polygon = n – 2 n Where n means number of side Examples 1. The sum of the angles of a polygon is 12600. How many sides has the polygon? 0 Solution Sum of the angles of a polygon = (n – 2) x 180 1260 = 180n - 360 180n = 1260 + 360 180n = 1620 Divide both sides by 180 n= n = 9sides 1620 180 2. Find the sum of the interior angles of a regular heptagon. Solution Sum of the angles of a polygon = (n – 2) x 180 Heptagon (n) = 7 Sum of the angles of a polygon = (7 – 2) x 180 = 5 x 180 = 900 0 0 0 3. Calculate the size of each angle of a regular Octagon. Solution Sum of the angles of a polygon = (n – 2) x 1800 Octagon (n) = 8 = (n – 2) x 1800 = (8 – 2) x 180 = 6 x 180 = 10800 Each sizes = 1080 0 = 135 8 Class work 1. Find the sum of the interior angles of heptagon. 2. Calculate the size of each angle of a regular 15 sided polygon. 3. Each of the interior angles of a regular polygon is 1080. How many sides has the polygon?