SOLUTION: Find the measure of one interior angle of a regular nonagon. Round to the nearest tenth, if necessary.

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Question 1175920: Find the measure of one interior angle of a regular nonagon. Round to the nearest tenth, if necessary.
Found 2 solutions by Theo, ankor@dixie-net.com:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
a nonagon is a 9 sided polygon.

if it's regular, then all sides are the same measure and all angles are the same measure.

you can find the measure of one internal angle in two distinct ways.

first way is to find the measure of each external angle.

the external angle of a polygon is the supplement of its corresponding internal angle.

the sum of the external angles of a polygon is always equal to 360 degrees.

if the polygon is a regular polygon, then the measure of each external angle is 360 / the number of sides of the polygon.

360 / 9 = 40 degrees.

the supplement of 40 degrees is 180 - 40 = 140 degrees.

that's the measure of each internal angle of the regular nonagon.

the other way is to use the formula for the sum of the internal angles of a polygon.

that formula is that the sum of the internal angles of a polygon is equal to 180 * (n-2), where n is the number of sides of the polygon.

using that formula, you get the sum = 7 * 180 = 1260 degrees.

divide that by 9 to get each internal angle of a regular nonagon = 1260 / 9 = 140 degrees.

you get the same answer either way.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Find the measure of one interior angle of a regular nonagon.
a nine sided figure
n = 9
A =
A = 140 degrees