Question

If one of the interior angles of a regular polygon is found to be equal to $\frac{9}{8}$ times of one of the interior angles of a regular hexagon, then the number of sides of the polygon is

Answer 1

Let the interior angle of regular polygon be x. According to the question,
$x^{\circ }=\frac{9}{8}\times {120}^{\circ }={135}^{\circ }$
${135}^{\circ }=\frac{(n-2)\times {180}^{\circ }}{n}$
$45n=$${360}^{\circ }$
Hence, the number of sides is $8$.