Question

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

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

Answer 1

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)`