Question

1. An exterior angle and the interior angle of a regular polygon are in the ratio 2:7. Find the number of sides in the polygon?

Answer 1

Answer:

Let exterior and interior angle of a polygon be 2x and 7x respectively

Exterior angle + Interior angle = 180°

2x + 7x = 180

9x = 180

x = $\frac{180}{9}$

x = 20

Exterior angle = 2x = 2 × 20 = 40°

Interior angle = 7x = 7 × 20 = 140°

No. of sides = 180 - 140

                    = 40

                    = $\frac{360}{40}$

                    = 9

∴ The polygon has 9 sides