Question: Octagon Angle

Comment on Octagon Angle

For this one, I found the value of the outside angle by doing 360/8= 45, then subtracted the value from 180 to get 135. Would this work with any polygon or did I get lucky?
greenlight-admin's picture

Great reasoning, Marlon!
Yes, that technique will always work. Here's why.

We know that the sum of the angles in an n-sided polygon = 180(n - 2)
So, if we have a REGULAR n-sided polygon, the measurement of each angle = 180(n - 2)/n
Now take: 180(n - 2)/n
Expand to get: (180n - 360)/n
Rewrite as: 180n/n - 360/n
Simplify: 180 - 360/n

In your solution, you take 360/n and subtract this from 180 degrees.
In other words, the measurement of each angle = 180 - 360/n, which is the same as the expression we derived from the formula.

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