Answer:
n=8
Solution,
Interior angle of regular polygon of n sides:
[tex] \frac{(n - 2)180}{n} [/tex]
Exterior angle of regular polygon of n sides:
[tex] \frac{360}{n} [/tex]
Given,
[tex] \frac{ \frac{360}{n} }{ \frac{(n - 2)180}{n} } = \frac{1}{3} \\ or \: \frac{360}{(n - 2)180} = \frac{1}{3} \\ or \: \frac{360}{180n - 360} = \frac{1}{3} \\ or \: 180n - 360 = 360 \times 3 \\ or \: 180n - 360 = 1080 \\ or \: 180n = 1080 + 360 \\ or \: 180n = 1440 \\ or \: n = \frac{1440}{180} \\ n = 8[/tex]
Hope this helps...
Good luck on your assignment..
