How do you find m in terms of n, supposing that angle CEF is the interior angle of another regular polygon with m sides?

Question

angle CEF = #(720 degrees)/n# as a function of n

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Answer 1 · 2018-04-30T14:46:01

Total of #m# interior angles of a polygon of m sides will be #(2m-4)*90^@#.

Given that angle CEF is the interior angle of a regular polygon with m sides.

We can write

#angleCEF=[(2m-4)*90^@]/m#

Again it is given #angleCEF=720^@/n#

Hence

#angleCEF=720^@/n=[(2m-4)*90^@]/m#

#=>720^@/n=[(2m-4)*90^@]/m#

#=>8/n=(2m-4)/m#

#=>8/n=2-4/m#

#=>4/m=2-8/n#

#=>2/m=1-4/n#

#=>2/m=(n-4)/n#

#=>m=(2n)/(n-4)#