Geometry: Finding Polygon Sides, if only given one interior angle, Regular Polygon?

Question

How do i find how many polygon sides if only given one interior angle?

Answer 1

If you know the interior angle, find the exterior angle which is its supplement.



Since the sum of the exterior angles is always 360 degrees, divide 360 by that measure. If it is a whole number, that is the number of angles, and the number of sides.



Ex: int angle= 160 for a regular polygon.

ext . Angle= 180-160= 20



360/20= 18

18 sides



Hoping this helps!

Answer 2

The sum of the interior angles of any convex polygon with n sides is 180(n - 2).

You are told that it is a regular polygon, so you know that all the angles are the same.

An n sided polygon also has n interior angles.



So if a is the measure of one angle, then

a * n = 180(n - 2)

a * n = 180n - 360

a * n - 180n = -360

180n - a * n = 360

(180 - a)n = 360

n = 360 / (180 - a)

Answer 3

The easy way is to use the interior angle to find the exterior angle (it's the supplement...in degrees that's 180-x, where x is the interior angle measure in degrees). The sum of exterior angles is always a full circle, so n*(180 - x) = 360. Solve that for n:



n = 360 / (180 - x) = 2 / (1 - x/180)



For radians, that becomes n = 2 / (1 - x/pi)