Given a polygon with 18 sides, find the sum of the measures of its interior angles.  A polygon with 18 sides has an interior angle measure sum of ______°.  

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

The answer is 180°*16 = 2880°.

The general formula is Sa=180°*(n-2) for any polygon with n sides.

This formula may be proved relatively easy for convex polygons. Consider a point P in the interior of the polygon and draw segments from this point to all vertices.

We obtain n triangles, each has the sum of angles 180°. The sum of angles whose vertex isn't P is the sum of interior angles of the polygon. The sum of angles whose vertex IS P is one complete circle, i.e. 360°.

So we have 180°*n=Sa+360°, or Sa=180°*(n-2).

This theorem holds for concave polygons also but the proof is more difficult.

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mathace | (Level 3) Assistant Educator

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The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180.

`S=(n-2)*180`

`S=(18-2)(180)`

S=16(180)

S=2880

A polygon with 18 sides has an interior angle sum of 2880 degrees.

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Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

Sum of interior angles = `180(n-2)`

In this equation, n equals the number of sides of the polygon that you are trying to find the sum of interior angles for.

So, in this case, you would substitute n as 18, because the number of sides is 18.

`180(18-2)`

`180(16)`

`180 * 16`

`2880` = Sum of interior angles

If you ever forget this formula, use this little method I just devised right now that should help:

What are the interior angle measures of a square? There are four angles in a square, and each of them is a right angle. That means the sum of interior angles for a square is 360.

Now, you can see how you can use this equation to get that number. It can remind you of the setup of the equation if you look at it like this.

So, a square has 4 sides. You subtract 2 (the n-2 in the equation) and get 2. Then you multiply that by 180 and you get 360 degrees!

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loves2learn | (Level 3) Salutatorian

Posted on

For questions relating to the sum of angles given a certain number of sides, there is a specific formula:

`180(n-2) `

Where n is the number of sides. This result will give you the how many degrees are in that figure.

So, plugging in what we know, you get

`180(18-2) `

Simplify,

`2880 `

Therefore, there are `2880^o `  in this polygon with 18 sides

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dirgha702 | eNotes Newbie

Posted on

Hi, 

for a polygon 

to find the sum, there is a formula as  

`S = (n-2)*180`

`S= (18-2)*180`

`S = (16)*180`

`S= 2880`

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