Sagot :
Answer:
12 side polygon
Step-by-step explanation:
Interior angle of n side regular polygon: = ((n-2)x180)/n
((n-2)x180)/n = 150
(n-2)x180 = 150n
180n - 360 = 150n
30n = 360
n = 12
check: (12-2)x180/12 = 150
Answer:
The polygon has 12 sides (a dodecagon).
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]
We are given the interior angle of 150°, thus:
[tex]\displaystyle \frac{180(n-2)}{n}=150[/tex]
Multiplying by n:
[tex]\displaystyle 180(n-2)=150n[/tex]
Operating
[tex]\displaystyle 180n-360=150n[/tex]
Rearranging and simplifying:
[tex]\displaystyle 180n-150n=360[/tex]
[tex]\displaystyle 30n=360[/tex]
[tex]n=360/30=12[/tex]
n = 12
The polygon has 12 sides (a dodecagon).