Hexagon

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hexagon

Shown above is a regular hexagon. A regular hexagon has six sides of equal length, each couple intersecting to form a vertex of which there are six. This polygon has six internal angles of equal measure and has six external angles of equal measure.

Exterior and Interior angles

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Characteristics of a regular hexagon:

	Number of sides = 6:
	Number of vertices = 6:
	Interior angle = 120�:
	Exterior angle = 60�:
	Exterior angle multiplied by the number of sides = 360�. (60� X 6 = 360�):

Number of sides = number of vertices:

Now ask yourself how might you find the the internal angle and the external angle of this regular hexagon and every other regular polygon of which there are an infinite number.

Take the first three regular polygons that have been encountered so far, the external angle of the equilateral triangle is 120�, multiply this by the number of sides or vertices on the triangle and the calculation should read as follows -- 120� x 3 = 360�.
Likewise with the square, its external angle is 90� and it has four sides, thus leading to a calculation again of the external angle of the square multiplied by the number of sides on the square -- 90� x 4 = 360�.
Taking into consideration the regular pentagon, it has five sides and an external angle of 72� and when multiplied, one by the other -- 72� x 5 = 360�.
What can be concluded from this is that when the exterior angle of a regular polygon is multiplied by the number of sides of the polygon the answer will always be 360�.
Letting Ea = Exterior angle and n = number of sides or vertices, for any regular polygon, Ea x n = 360� hence, Ea = 360�/n .
So for the regular hexagon shown above n = 6, thus leading to an external angle of Ea, when Ea = 360�/n then Ea = 360�/6 and Ea = 60�.