Question

Dina is making a logo and she decides to use a regular polygon. Each interior angle of the polygon measures 140°. What is the number of sides of this polygon?

Answer 1

The polygon has 9 sides (a regular nonagon).

Explanation:

Angles in a Regular Polygon

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures

`\displaystyle (180(n-2))/(n)`

The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:

`\displaystyle (180(n-2))/(n)=140`

Multiply by n:

`180(n-2)=140n`

Operate:

`180n-360=140n`

Reducing:

`40n=360`

Solving:

n=9

The polygon has 9 sides (a regular nonagon).