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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

Find the measure of one interior angle andthe measure of one exterior angle in eachregular polygon Write the equations andsolve showing ALL the workNonagon class=


Answer :

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°

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