Answer:
12
Step-by-step explanation:
Its interior angle has measure 150∘. Therefore, the exterior angle has measure 180∘−150∘=30∘. Therefore, the number of sides of the regular polygon with interior angle 150∘ is 12.
The sum of the interior angles of a regular polygon is given by:
180∘n-360
Where n is the number of sides.
Lets call the sum S
Then:
180∘n−360=S [1]
If the sum of interior angles is S, then each angle is:
S/n
We are given 150∘ for each angles. So,
S/n=150∘[2]
From [2]
S=150n
Substituting in [1]
180n−360=150n
30n=360⇒n=12
The polygon has 12 sides.
