Sum of exterior angles of a regular polygon

The angle between a side of a polygon and an extended adjacent side gives an exterior angle of a polygon. It is an angle formed by a transversal as it cuts one of two lines and is situated on the outside of the line.

A polygon close polygon A polygon is a 2-dimensional closed shape with straight sides, eg triangle, hexagon, etc. Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is:. Calculate the size of the interior angle of a regular hexagon close hexagon A polygon with six sides. If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.

Sum of exterior angles of a regular polygon

Exterior angles of a polygon are formed when by one of its side and extending the other side. The sum of all the exterior angles in a polygon is equal to degrees. You are already aware of the term polygon. A polygon is a flat figure that is made up of three or more line segments and is enclosed. The line segments are called the sides and the point where two sides meet is called the vertex of the polygon. The pair of sides that meet at the same vertex are called adjacent sides. An angle at one of the vertices is called the interior angle. The internal and exterior angles at each vertex varies for all types of polygons. Now, let us learn in detail the concept of its exterior angles. An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side. See the figure below, where a five-sided polygon or pentagon is having 5 vertexes. The exterior angles of this pentagon are formed by extending its adjacent sides. Let us say you start travelling from the vertex at angle 1.

We already know two of them. Practice exterior angles of a polygon questions. How to solve problems involving exterior angles.

An exterior angle of a polygon is the angle that is formed between any side of the polygon and a line extended from the next side. Every polygon has interior and exterior angles. The exterior is the term opposite to the interior which means outside. Therefore exterior angles can be found outside the polygon. Any flat shape or figure is said to have interior or exterior angles only if it is a closed shape. For example, a triangle is a polygon, which satisfies this condition.

You can view the exterior angle of a polygon by extending one of the sides of a polygon and looking at the angle between the extension and its adjacent side. All polygons follow a rule that the sum of their exterior angles will equal degrees. Although you could draw two exterior angles at each of the polygon's vertices, this rule applies by taking the sum of only one exterior angle per vertex. This rule is important in that it helps to determine other aspects of the polygon, such as the measurements of each external angle, each internal angle, and the number of sides the polygon has. The angles of a regular polygon are equivalent, and their sides are as well. The sum of the exterior angles of a regular polygon will always equal degrees. To find the value of a given exterior angle of a regular polygon, simply divide by the number of sides or angles that the polygon has. The sum of the exterior angles of an irregular polygon also equals degrees, even though the angles are not equivalent.

Sum of exterior angles of a regular polygon

So, if the polygon has n sides, then. Solved examples on sum of the exterior angles of a polygon:. If the polygon has n sides,.

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Maths: Exam-style questions Personalise your Bitesize! An angle is formed between two lines or line segments. United States. Watch Now. Privacy Policy. Exterior Angles of a Polygon Example 1: Find the measure of the exterior angles of an 8 sided regular polygon. A regular polygon has 15 sides. The polygon in which the sum of all the exterior angles is equal to the sum of all the interior angles is called Quadrilateral. A polygon whose sides are not all the same length or whose interior angles do not all have the same measure. Exterior Angle of Regular Polygon By its property, any regular polygon has equality in its attributes. Learn Math Formulas with tutors mapped to your child's learning needs. This can be understood clearly by observing the exteriors angles in the below triangle.

The sum of the angles in a polygon depends on the number of edges and vertices. There are two types of angles in a polygon - the Interior angles and the Exterior Angles.

United States. Whole Number. The angle between a side of a polygon and an extended adjacent side gives an exterior angle of a polygon. Important Physics Formulas. Are exterior angles always degree? Let us take a look at the figure in which a quadrilateral has 4 unequal sides and angles. United States. What is the exterior angle of a 12 sided polygon? Exterior angles of a polygon GCSE questions. Thus, although the sum of a Also, read about Geometric Shapes here. Download Now. We have already seen that,.