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

Answer:

The polygon has 9 sides (a regular nonagon).

Step-by-step 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

$\displaystyle \frac{180(n-2)}{n}$

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

$\displaystyle \frac{180(n-2)}{n}=140$

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).