Question 290917
<pre><font size = 4 color = "indigo"><b>
The fotmula for the sum of the interior angles of
any n-sided polygon is (n-2)*180°, and since
a regular polygon has n congruent interior angles,
each one has {{{((n-2)*"180°")/n}}}

You can't have 3 sides because a regular 3-sided polygon is an
equilateral triangle, which has 60° interior angles.

{{{drawing(200,200,-1.5,1.5,-1,2,triangle(-1,0,1,0,0,sqrt(3)) )}}}

You can't have 4 sides because a regular 4-sided polygon is a
square, which has 90° interior angles.

{{{drawing(200,200,-1.5,1.5,-1,2,rectangle(-1,-.5,1,1.5) )}}}

So you must have 5 sides because a regular pentagon has
108° interior angles, and a 108° angle is an obtuse angle.  

{{{drawing(200,200,-1.7,1.7,-.1,3.3,

line(-1,0,-1.618033989,1.902113033),

line(1,0,1.618033989,1.902113033),

line(-1.618033989,1.902113033,0,3.077683537),

line(1.618033989,1.902113033,0,3.077683537),

line(-1,0,1,0)

)}}}

Maybe your teacher wants you to do it this way:

Since an obtuse angle is one greater than 90°
You could get the answer by the inequality

{{{((n-2)*"180°")/n>"90°"}}}

Multiply through by n.  Since n is positive,
we do not reverse the inequality:

{{{(n-2)*180>90n}}}

{{{180n-360>90n}}}

{{{180n-90n>360}}}

{{{90n>360}}}

{{{n>4}}}

So the smallest integer greater than 4 is 5.

Edwin</pre>