Answer:
The polygon has 15 sides
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 in a regular polygon, each angle measures
[tex]\displaystyle \frac{180(n-2)}{n}[/tex]
The regular polygon's interior angle is 156°, thus
[tex]\displaystyle \frac{180(n-2)}{n}=156[/tex]
Multiply by n:
[tex]180(n-2)=156n[/tex]
Operate:
[tex]180n-360=156n[/tex]
Reducing:
[tex]24n=360[/tex]
Solving:
[tex]n=15[/tex]
The polygon has 15 sides
