A regular polygon has 150∘ as the size of each interior angle. How many sides does it have?
Answer Details
A regular polygon has equal interior angles and equal sides. The sum of the interior angles of a polygon with n sides is (n-2) times 180 degrees. So, if a regular polygon has interior angles of 150 degrees, we can use this formula to find the number of sides:
(n-2) x 180 = sum of interior angles of the polygon
(n-2) x 180 = 150n
Simplifying the equation:
n - 2 = 150/180 * n
n - 2 = 5/6 * n
n = 12
Therefore, the regular polygon has 12 sides.
Answer: 12.