Question

Find the measure of each exterior angle of a regular nonagon.

Answer 1

Because it is a regular polygon, at each corner you change direction by the same angle (x degrees, the measure of the exterior angles, as marked in the figure). As you get back to point A, you have changed direction 9 times, for a total angle, in degrees of
9x=360
x=360/9=40

Answer 2

40 would be the answer than, right?

Answer 3

notice that the exterior angle is just the supplementary angle of the interior angle. trying to add all the exterior angles you'll have 90+90+90+90=360.
let's check for a pentagon. the interior angle for a pentagon is: (5-2)(180) = 540
divide by the number of sides 540/5 = 108.. the supplementary angle would be 180-108=72.. since there are 5 sides then 72*5=360.. is it proof enough for the sum of exterior angles? =)