Question

Find the measure of one interior angle andthe measure of one exterior angle in eachregular polygon. Write the equations andsolve showing ALL the work.Nonagon

Answer 1

Angles in a nonagon

A regular nonagon is a 9-sided polygon with all of its sides and angles of the same measure.

The sum of the interior angles in a n-sided polygon is:

S = 180*(n-2)

And each internal angle has a measure of:

I = S/n = 180*(n-2)/n

For n=9:

I = 180*7/9=140°

Since the sum of all exterior angles of ANY polygon is 360°, each exterior angle of a nonagon is 360/9 = 40°

Answer: Internal angle=140°. External angle=40°