Polygon Mania

Sum of the interior angles of a polygon = $180^\circ (n - 2)$ . Therefore, $\frac{n}{2} \Big( 2a + (n - 1)d \Big) = 180^\circ (n - 2)$ $\frac{n}{2} \Big( 240 + (n - 1)5 \Big) = 180^\circ (n - 2)$ $\frac{5n}{2} \Big( 48 + n - 1 \Big) = 180^\circ (n - 2)$ $\frac{n}{2} \Big( 47 + n \Big) = 36^\circ (n - 2)$ $47n + n^2 = 72n - 144$ $n^2 - 25n + 144 = 0$ $n^2 - 16n - 9n + 144 = 0$ $(n-9)(n-16) = 0$ Therefore, either $n = 9$ or $n = 16$