Question 247321
what is the number of sides a polygon has if the sum of the degree measures of the interior angle is 180°?
<pre><font size = 4 color = "indigo"><b>
The formula for the {{{S}}}, the sum of the degree measures of the interior
angles of a polygon with {{{n}}} sides is 

{{{S=(n-2)*"180°"}}}

So we substitute {{{"180°"}}} for {{{S}}}

{{{"180°"=(n-2)*"180°"}}} 

Divide both sides by {{{180°}}}

{{{"180°"/"180°"=(n-2)*"180°"/"180°"}}}

{{{1=n-2}}}

{{{3=n}}}

So the answer is:  It has 3 sides.

That means the polygon is a triangle.  

I'll bet you've known all along that the 

measures of the interior angles of a triangle

is 180°, now haven't you?  Maybe you didn't

know that a triangle was a polygon, but it is!

It's a polygon with three sides!

Edwin</pre>