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9 sided polygon - Computers & Internet

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'enneagon' or 'nonagon'

Posted on May 13, 2014


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How many angles does a regular polygon have when its interior angle is 176 degrees


Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
-----------
n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

1 Answer

How many sides does a regular polygon have when the interior degrees is 176?


Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
-----------
n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

1 Answer

Names of all polygons


Since there are an infinite number of polygons, I can't list all of their names. For the names of all polygons with up to 100 sides, see http://en.wikipedia.org/wiki/Polygon

Jun 05, 2014 | Computers & Internet

1 Answer

Sslc maths


What follows is true for CONVEX polygons.
Let n be the number of sides of a convex polygon, and let n be greater than or equal to 4, then
The number of diagonals is given by n*(n-3)/2
Using this rule, write n*(n-3)/2=20. Clear the fraction, open brackets. You end up with n^2-3n-40=0.
Factor the polynomial or use the formulas for the quadratic equation to find the roots as n=-5 or n=8. Discard the negative root because n must be positive.

Oct 05, 2013 | Computers & Internet

1 Answer

Polygons


The perimeter of a polygon is the length of its sides. The area is the space enclosed by the polygon.
The difference is similar to the difference between a fence around a yard and the space in the yard.

May 02, 2013 | Office Equipment & Supplies

1 Answer

What is a polygon with 15 diagonals


For convex polygons there is a relation linking the number of sides to the number of diagonals. Here it is, with n=number of sides
number of diagonals=n*(n-3)/2. Obviously the number of sides must be greater or equal to 3.
If you use the relation for a hexagon (n=6) the number of diagonals is 9. With n=7, the number of diagonals is 14, and for n=8 the number of diagonals is 8*(8-3)/2=20. The answer is that there does not exist a CONVEX polygon with 15 diagonals.
You can also try to solve the quadratic equation n(n-3)/2=15 for a positive integer. And you will not find a solution.
For polygons that are not convex there may be many solutions or no solutions. I leave that to you as an exercise.

Mar 11, 2013 | SoftMath Algebrator - Algebra Homework...

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