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.

answered Sep 6 "18 in ~ 19:57

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
how to acquire the minimum angle between two cross lines?
Rotation edge of continual polygon that has largest taxicab maginitude in between all vertices
finding the inner angle between two present of slopes $m_1$ and also $m_2$ indigenous a programming view
finding the coordinate of a point using a distance and also an angle from given suggest
ratio of locations of two octagons
discover intersection of 2 lines offered subtended edge
uncover the angle of a tangent line in between two circles
acquire the point out of a hexagon discovering only a what length each side have to be and a suggest
straightforward trigonometry + polygon geometry wherein am i going wrong?
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

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.