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 

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



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



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



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



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











So the smallest integer greater than 4 is 5.

Edwin