How to find the number of side a reg. polygon has

[lectromagnet94]

Okay,
Can someone please explain to me (kindly plz) how to find the number of side a regular polygon has if you know one interior angle?
I dont understand!!

 

[arthur ohlsten]

each interior angle subtends one side of the polynomial
360/ [interior angle] = number of subtended sides
Arthur

 

[Denis]

Question Sir L.M.:
Draw a circle.
From its center, draw 5 radius lines such that the 5 angles created at center are equal.
What is the size of these angles?

If you don't know that, then you're asking us to teach you a lot of stuff that you have to know
in order to understand, which can only be done in a classroom environment.
So this is why we "as politely as possible(!)" suggest that we're not in a position to do this.

None of the volunteer tutors here are interested in typing out multiple pages of stuff that
are required in order to "teach".

Kapish? How's your Tylenol supply?

By the way, if you can't see why drawing a circle is related to your question, then you're not
ready for that question.

 

[fasteddie65]

The formula for the measure of an interior angle of a regular polygon of n sides is (n - 2)/180/n.

 

[mmm4444bot]

The formula for the measure of an interior angle of a regular polygon of n sides is (n - 2)/180/n.

Hello Eddie:

Are you sure that's the formula? I tried using it on a square (n = 4).

Your formula gives me an interior angle of 1/360th of a degree. I was expecting to get 90 degrees.

Perhaps, you could show me how it works.

MY EDIT: Nevermind, Eddie; Arthur posted a formula that works. :wink:

 

[arthur ohlsten]

A square has 4 sides.
360/4 = 90 degrees
each interior angle =90 degrees

if a polygon has n sides each interior angle would be 360/n.

Arthur

 

[wjm11]

Can someone please explain to me (kindly plz) how to find the number of side a regular polygon has if you know one interior angle?

Hello, Lectromagnet,

If some of the posts above seem confusing, I believe it’s because of varying interpretations of “interior angle.” I interpret “interior angle” to mean the angle formed at each vertex.

With that in mind, here is a simple approach:

First find the exterior angle; i.e., subtract the interior angle from 180.

Note that the sum of the exterior angles must equal 360, so simply divide 360 by the exterior angle. It’s that simple.

Formula (where n is the number of sides):

n = 360/(180 – interior angle)

Example: interior angle equals 120 degrees. Therefore, exterior angle equals 60 degrees. 360/60 = 6. The polygon is a hexagon.

 

[mmm4444bot]

If some of the posts above seem confusing, I believe it’s because of varying interpretations of “interior angle.”

Actually, wjm, I believe it's because they're both wrong. Thus my comments to both authors.

I cannot remember seeing Fast Eddie return to his erroneous posts after I comment. I'm not sure he gets e-mail notifications; he may not follow-up. (I suspect Fast Eddie's motivation for posting has less to do with helping original posters and more to do with a need for some sort of self-validation.)

Anyway, his formula has a typo. The correct formula for the interior angle (I) follows.

I = (n - 2)*(180/n)

When I need to remember a formula for the interior angles, I think of 360/n as the central angle, this angle opposite a side which forms an isoceles triangle. The two remaining angles are (1/2)*(180 - 360/n), but, of course, the interior angle is just the sum of these; therefore, I end up with the following.

I = 180 - 360/n

Both my correction of the formula posted by the fast one and my own are algebraic manipulations of yours.

Cheers,

~ Mark