If the polygon shown below is a regular nonagon what is the value of x?

The sum of the measures of the angles of a polygon is given by (n - 2)(180), where n is the number of sides.  In this case we would have (9-2)(180)=7(180)=1260.  This is the sum of the angles.  Since it is a regular nonagon, that means that all sides are congruent and all angles are congruent.  Therefore we find the measure of each individual angle by dividing the sum, 1260, by the number of sides, 9.  1260/9=140.  x forms a linear pair with one of the interior angles; that means that the interior angle, 140, added to x would give us 180.  Therefore we find x by subtracting 180-140. x = 40.