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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.

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