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You are watching: What is the central angle of a hexagon
The main angle that a consistent polygon is formed by 2 lines native consecutive vertices come the centre allude or two radii of continually vertices that the circumsribed circle.
I can plot each suggest on the hexagon by utilizing the same length of radii and rotating $60$ levels from the center.
I know I have the right to work the end the exterior edge by $(n−2) cdot 180^circ$.
That offers me $720 / 6 = 120$, and also $180 - 120 = 60$.
Is there any connection between the central angle and the exterior angle?
As solution to your concern on comments, notice that when we attract a heat from a peak to facility of a consistent polygon, the line is angle bisector that an internal angle, say internal angle is $2alpha$. In a triangle constructed this way, there room two such $alpha$ angles, so main angle is $180 - 2alpha$. But notice that this is as exact same as the exterior angle. Thus this is not distinct to hexagon. Below is a lay out for a basic result:
For a continuous $n$-gon the main angle is $frac 360n$.
The central angles cut the $n$-gon into $n$ isoceles triangles. So that base of these triangles room $frac 180 - frac 360n2 = 90 - frac180n$. The interior angles are two of these base angle so the interior angles $180 - frac 360n$.
And there because that the exterior angles space $180 - (180 - frac 360n) = frac 360n$.
So this is true no matter what consistent $n$-gon girlfriend do.
See more: Why Was Elvis Called The King, Elvis Presley … The King Of Rock 'N' Roll
Hexagons and $60$ levels are specifically important number as represent the sides and radius being equal and tesselates the plane.
answered Sep 6 "18 in ~ 19:57
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