What is #n# if each interior angle of a regular #n#-gon measures 172.8°?

1 Answer
Mark Kononov
Dec 1, 2015

#n=50#.

Explanation:

I start out with the equation, #180(n-2)=172.8#.
However, I know that 172.8 is not the sum but an individual angle so I change the equation to #180(n-2)=172.8n#. I distribute to get #180n-360=172.8n#. I then go and subtract 172.8n on both sides while adding 360 on both sides to get #7.2n=360#. I divide 7.2 on both sides and ultimately get #n=50#.

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