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
[tex]\displaystyle \frac{180(n-2)}{n}[/tex]
The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:
[tex]\displaystyle \frac{180(n-2)}{n}=140[/tex]
Multiply by n:
[tex]180(n-2)=140n[/tex]
Operate:
[tex]180n-360=140n[/tex]
Reducing:
[tex]40n=360[/tex]
Solving:
n=9
The polygon has 9 sides (a regular nonagon).
