how can i calculate the number of sides a polygon has if i am given one of the intereior angles....e.g 127????

Answer 1

If it is a regular polygon (all sides and agles same) Hmmm

In an equilateral triangle, the interior angles add up to 180°. But in a square, they add up to 360° In a hexagon, the interior angles are 120°, and add up to 720°.

Best I can think of right now is find the least common multiple of your angle and 180°

Answer 2

First off, you can't unless it is a regular polygon. For example, a right tirangle has a 90 degree angle in it and so does a square.

So lets assume its a regular polygon. Here is the formula

Angle = (n-2) *180/n where n is the number of sides for a regular polygon (all sides equal length).

So, for a square it would be (4 - 2) * 180/4 = 360/4 = 90 for every angle, triangle is (3-2) * 180/3 = 60 degrees

So enter your angle and solve for n --
Angle * n = 180 * n - 360
127n = 180n -360 or 53n = 360
n would be the nearest whole number to 360/53 i.e. 7

Answer 3

There are two methods:
1. Each angle in a regular polygon = (n-2)*180/n, so set the formula = 127 and solve.

(n-2)180 = 127n
180n - 360 = 127n
53n = 360
n = 6.79 (this is not possible, since n must be an integer.)

2. Each interior angle is the supplement of the corresponding exterior angle, and the sum of the exterior angles is always 360, so divide 360 by the exterior angle to find how many there are.

180 - 127 = 53.
360/53 = (again this gives an impossible answer)

as another example:
See if you can find the answer if the interior angle = 108.

(the answer should be 5)

Answer 4

It's a little more complex than simply dividing into 360 degrees.

Consider:
Triangle (3 sides); all add up to 180 degrees; in equilateral triangle, all angles are 60 degrees.

Square (4 sides); all add up to 360 degrees; all angles are 90.

Pentagon (5 sides); all add up to 540 degrees; all angles are 108.

General pattern: sum of angles in any regular polygon is:
180 x (n-2) where n= number of sides.

The "reciprocal" (that is, determining number of sides from given angle) comes from following formula:

[180 x (n-2)] / n = x
where x = each angle (in this case, 127)

Try it, and good luck!

Answer 5

i assume you are talking about regular polygons (in which case 127 degree of interior angle does nt work! :P)

This work for all number of sides for regular polygons;

If you extend one side of polygon to make a long straight line, you can find the outside angle (as opposed to the interior angle). This is simply done by subtracting the interior angle with 180.

So outside angle = 180 - interior angle.

The rule is, the TOTAL outside angle for all sides of the polygon is ALWAYS 360.

So if you have a polygon with 156 degrees of interior angles, you know that the outisde angle is 24 degrees. Therefore, the number of sides is simply 360/24 = 15. fifteen sides.

Answer 6

The sum of angles of a polygon = (n-2)*180
If it is a regular polygon then all the angles are equal

Take an example 120 each side

n*120 = (n-2)*180
==> 120n = 180n - 360
==> 60n = 360
==> n = 6


~~~
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Answer 7

If it's a regular polygon, divide the angle into 360.

Answer 8

360/(180-n)
n=interior angle

Answer 9

can you draw lines inside to make trainagles then use the pathagryam therom?

Answer 10

http://mathforum.org/library/drmath/sets/select/dm_area_irreg.html