Question

360÷n-1 =180 - 360÷n+2

Answer 1

Answer:

$\frac{360}{n - 1} = 180 - \frac{360}{n + 2} \\ \\ 360( \frac{1}{n - 1} + \frac{1}{n + 2} ) = 180 \\ \\ \frac{n + 2 + n - 1}{(n - 1)(n + 2)} = \frac{1}{2} \\ \\ \frac{2n + 1}{ {n}^{2} + n - 2} = \frac{1}{2} \\ \\ 4n + 2 = {n}^{2} + n - 2 \\ \\ {n}^{2} - 3n - 4 = 0 \\ \\ {n}^{2} - 4n + n - 4 = 0 \\ \\ n(n - 4) + 1(n -4 ) = 0 \\ \\ n = - 1 \: \: \: \: n = 4$