Question

How do we find the measure of EACH exterior angle and the measure of EACH interior angle of any polygon?

Answer 1

A rule of polygons is that the sum of the exterior angles always equals 360 degrees, for more easly understanding just take a an example, for a regular octagon (8-sides).

First we must figure out what each of the interior angles equal. To do this we use the formula:

((n-2)×180)/n where n is the number of sides of the polygon. In our case n=8 for an octagon, so we get:

((8-2)×180)/8 => (6×180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees.

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees.

And since there are 8 exterior angles, we multiply 45 degrees ×8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.