Question

Each exterior angle of a regular polygon is 9°

Calculate the number of sides of the polygon​

Answer 1

Required Answer :-

Let the number of sides=x

• Each angle measures 9°

As we know that in a polygon

`{\boxed{\sf Sum\;of\:exterior\:angles=360°}}`

• Substitute the values

`{:}\longrightarrow`
`\sf 9x=360`

`{:}\longrightarrow`
`\sf x={\frac {360}{9}}`

`{:}\longrightarrow`
`\sf x=40`

`\therefore`Number of sides=40.

Answer 2

40

Explanation:

The sum of the exterior angles of a polygon = 360°

Divide this by the value of 1 exterior angle to find the number of sides n

n = 360 ÷ 9 = 40