Want to boost this question? add details and clarify the trouble by editing and enhancing this post.

Closed 3 year ago.

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.


re-publishing
mention
follow
answered Sep 6 "18 in ~ 19:57
*

fleabloodfleablood
1
$endgroup$
include a comment |

Not the price you're looking for? Browse other questions tagged trigonometry or questioning your own question.


The Overflow Blog
Featured on Meta
related
3
how to acquire the minimum angle between two cross lines?
1
Rotation edge of continual polygon that has largest taxicab maginitude in between all vertices
1
finding the inner angle between two present of slopes $m_1$ and also $m_2$ indigenous a programming view
1
finding the coordinate of a point using a distance and also an angle from given suggest
0
ratio of locations of two octagons
0
discover intersection of 2 lines offered subtended edge
1
uncover the angle of a tangent line in between two circles
0
acquire the point out of a hexagon discovering only a what length each side have to be and a suggest
2
straightforward trigonometry + polygon geometry wherein am i going wrong?
1
how to calculation the angle between a rotating reference allude and a revolution remote allude at any type of degree that rotation?
warm Network questions much more hot concerns
*

gaianation.net
company
ridge Exchange Network
site style / logo © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.28.40592


gaianation.netematics stack Exchange works finest with JavaScript allowed
*

her privacy

By clicking “Accept every cookies”, you agree ridge Exchange have the right to store cookie on your an equipment and disclose info in accordance v our Cookie Policy.