Question

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

• A. 5
• B. 8
• C. 7
• D. 4

Answer 1

The correct option is B 8

et the number of sides of a regular polygon are n and one of the interior angles is αα.
∴α=(2n−4)×90∘n=98×(2×6−4)×906∴α=(2n−4)×90∘n=98×(2×6−4)×906
⟹2n−4=n×32⟹n=8