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

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

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

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

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

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

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

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

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