1-ANGLES OF A POLYGONE(Selfmade)

8/8/2019 1-ANGLES OF A POLYGONE(Selfmade)

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Angles of a polygonPOLYGON:-A polygon is a 2-dimensional closed shape with straight sides.

In this section we will revise the properties of polygons.Regular and irregular polygons:-1The simplest polygon is a triangle (a 3-sided shape).2Polygons of all types can be regular or irregular.3A regular polygon has sides of equal length,

and all its interior angles are of equal size.

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Irregular polygons can have sides of any length and angles of any size.5Here are the names of some common polygons:* regular triangles and regular quadrilaterals have special names.* All other regular polygons are simply termed 'regular pentagon','regular hexagon' etc.
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Rhombus:-1Diagonally opposite angles are equal.2All of its sides are ofequal length.3Opposite sides are parallel.4Diagonals bisect each other at 90.5It has 2 lines of symmetry.6Order ofrotational symmetry: 2.

Rectangle:-1All angles are equal (90).2Opposite sides are ofequal length.3Opposite sides are parallel.4The diagonals bisect each other.5The diagonals are equal in length.6It has 2 lines of symmetry.7Order ofrotational symmetry: 2.

Parallelogram:-1Diagonally opposite angles are equal.

2Opposite sides are ofequal length.3Opposite sides are parallel.4The diagonals bisect each other.5It has no lines of symmetry.6Order ofrotational symmetry: 2.

Trapezium:-1One pair of opposite sides is parallel.2It has no lines of symmetry.3It has no rotational symmetry.

Kite:-1Two pairs of sides are ofequal length.2One pair of diagonally opposite angles is equal.3Only one diagonal is bisected by the other.4The diagonals cross at 90.5It has 1 line of symmetry.6It has no rotational symmetry.

Angle properties of polygons:-

1-The formula for calculating the sum of the interior anglesof a regular polygon is: (n - 2) 180where n is the number of sides of the polygon.

2-This formula comes from dividing the polygon up intotriangles using full diagonals.

3- interior angles of a triangle add up to 180.4-For any polygon, count how many triangles it can besplit . Then multiply the number of triangles by 180.

5-This quadrilateral has been divided into two triangles,so the interior angles add up to 2 180 = 360.


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1-This pentagon has been divided into three triangles,so the interior angles add up to 3 180 = 540.

2-In the same way,a hexagon can be divided into 4 triangles,a 7-sided polygon into 5 triangles etc.

3-Can you see the pattern forming?The number of triangles = number of sides - 2.

1-The exterior angle of a polygon and its correspondinginterior angle always add up to 180

(because they make a straight line).2-For any polygon, sum of its exterior angles is 360.(You can see this because if you imagine 'walking' all theway round the outside of a polygon you make one fullturn.)

Calculating the interior and exterior angles of regularpolygonsFinding the interior angle:-1-Formula Sum of Interior angles= (n - 2) 180Example. A hexagon has 6 sides. So n = 6.

Using our formula from above, that gives us180(6-2) = 180(4) = 7200

Example. An octagon has 8 sides. So n = 8.Using our formula from above, that gives us180(8-2) = 180(6) = 10800

2-All the interior angles of a regular polygon are equal.3-Interior angle of a regular polygon = sum of

interior angles number of sidesQ- Find the interior angle of a regular hexagon.

Finding the exterior angle:-1- Exterior angles of a regular polygon always add up to360,

so the exterior angle of a regular hexagon isRemember : The interior angle and its corresponding

exterior angle always add up to 180. (For a hexagon, 120+ 60 = 180.)Q- Calculate the exterior angle of a regular octagon,and write down the value of the interior angle.


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1-ANGLES OF A POLYGONE(Selfmade)