Question

The ratio between the exterior angle and the interior angle of a regular polygon is 2 ratio 7.Find the number of sides in the polygon.

Answer 1

first no=2x
second no=7x.
sum of all sides of polygon =360
2x+7x=360
9x=360
x=40

Answer 2

Given :

• The ratio between the exterior angle and the interior angle of a regular polygon is 2 : 7 .

To find :

• The number of sides in the polygon .

Solution :

Let,

each exterior be x⁰ then , each of interior angle = (180⁰ - x⁰)

$\sf \frac{x}{180⁰ - x} = \frac{2}{7}$

$\sf⟹7x = 2(180⁰ - x) \\ \sf7x = 360⁰ - 2x \\ \sf9x = 360⁰ \: \\ \sf \: x = 40⁰$

∴ Number of sides in the Polygon

$\sf \: = \frac{360}{40} = 9$