How do I find the number of sides a polygon has when I know the angle sum?

Question

I use to know this, but haven't done it in a long time and now forgot.

The problem:
Find the number of sides of a convex polygon if the measure of its interior angles have a sum of 32,040 degrees.

If you could explain it too, that would be great.

--THX!

Answer 1

The angle sum is equal to 180*(n - 2), where n is the number of sides.

You can find this result by picturing each side of the polynomial being extended in one direction, as if they were trailing hairs that were being blown as the polynomial spins. Then draw the exterior angle at each vertex. Since traveling around the outside of the polynomial would result in completing a full circle, 360 degrees, it must be that the sum of these exterior angles is 360. Since the exterior angles form linear pairs with the interior angles, the collective sum of all the interior and exterior angles would be n*180, since each linear pair sums to 180 degrees. Since we know that the sum of the exterior angles is 360, the sum of the inteior angles must be n*180 - 360 = 180*(n - 2).

Answer 2

The rule to find the sum of internal angles is n - 2 x 180. Let n represent the number sides. Since you have been given the end result, simply work backwards, like if you're solving a simple linear equation. Divide by 180 and add 2, which gives you 24 sides. Also, the shape is called a icosikaitetragon. It's a simple question, and you probably could have solved it on your own.

Answer 3

The angle sum is 180(n-2). So since n = no.2 of sides we can isolate it using algebra...

(S = sum of angles btw...)

S = 180(n-2)
S/180 = n - 2
n = S/180 + 2

So..

n = 32,040/180 + 2
n = 180

So it would have 180 sides.

Answer 4

The formula is

(n - 2)180 = S , sum of the interior angles of convex polygon
(n - 2) = S/180
n = S/180 + 2

So, solving your problem,

n = 32,040/180 + 2
n = 180 sides ANS


Hope I help you.


teddy boy

Answer 5

i think the number of sides is related to sum of interior angles is sum of angles =(n-2)*180, so in this case you have 180 sides

Answer 6

89

Moving around an n-gon in general, the sum of the exterior angles can be any integer multiple of 360°.