For an 'n'-sided polygon, the number of diagonals can be calculated with this formula, n(n-3)/2.The sum of interior and exterior angles at a point is always 180º as they form a linear pair of angles.Interior angle = 180º(n-2)/n, where n refers to the number of sides. The angles of a regular polygon can be measured by using the following formulas:.Polygons are 2-D figures with more than 3 sides.An exterior angle can be calculated if the number of sides of a regular polygon is known by using the following formula:Įxterior Angle = 360º/n, where 'n' is the number of sides of the polygon Each exterior angle of a regular polygon is equal and the sum of the exterior angles of a polygon is 360°. Interior angle = 180º(n-2)/n, where 'n' is the number of sides Exterior Angles of a PolygonĮach exterior angle of a regular polygon is formed by extending one side of the polygon (either clockwise or anticlockwise) and then the angle between that extension and the adjacent side is measured. The value of an interior angle of a regular polygon can be calculated if the number of sides of the regular polygon is known by using the following formula: The number of interior angles is equal to the number of sides. The interior angles are formed between the adjacent sides inside the polygon and are equal to each other in the case of a regular polygon. All the exterior angles are equal (represented in yellow)Īs we learned above, there are two kinds of angles that can be found in the case of a regular polygon.All the interior angles are equal (represented in blue).All the sides of this regular hexagon are equal, i.e., AB = BC = CD = DE = EF = FA.Vertices of the hexagon: A, B, C, D, E, and F.Observe the figure of a regular hexagon given below to understand the parts of a regular polygon. In simple words, a regular polygon has all angles of the same measure at each vertex, and all sides of the same length while a polygon that has sides of different lengths and angles of different measures is referred to as an irregular polygon. Regular polygons are always convex, i.e., all the interior angles measure less than 180º. It is said that as per Euclidean Geometry, a polygon that is equiangular and equilateral is called a regular polygon while a polygon whose sides are not equiangular and equilateral is referred to as an irregular polygon. The difference between a regular and irregular polygon is given in the following table. Observe the table given below to see the names of different polygons as per their number of sides.ĭifference Between Regular and Irregular PolygonsĪ polygon can be categorized as a regular or irregular polygon based on the length of its sides and the measure of its angles. This shows that it is a shape that has three angles. For example, the trigon, also known as the triangle is made of two words 'tri' which means three, and 'gon' means angles. Each polygon is given a special name on the basis of its number of sides. The following chart shows the naming convention of polygons on the basis of the number of sides that they have. For example, a 3-sided polygon is a triangle, a 4-sided polygon is a quadrilateral, a 5-sided polygon is a pentagon, a 6-sided polygon is a hexagon, and so on. There are different types of polygons and they have different names depending on the number of sides that they have. The following section shows the different types of polygons along with their names based on the number of sides. For example, if a polygon has 3 sides, then it is called a triangle, whereas, if a polygon has 4 sides, it is a quadrilateral. The sides of a polygon define the name of the specific polygon because different polygons have different number of sides. The length of the sides of a polygon may or may not be the same.The angles in the polygon may or may not be the same.It is a two-dimensional figure, that is, it has only two dimensions length and width.It is a plane shape, that is, the shape is made of line segments or straight lines.A polygon is a closed shape, that is, there is no end that is left open in the shape.In other words, the following characteristics of a polygon help us to easily check whether a given shape is a polygon or not The properties of polygons help us identify them easily.
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