A regular polygon has an interior angle measure of 150°. How many sides does the polygon have?

For a regular polygon with n sides, each interior angle is given by:
((n - 2)180°) / n

Set this expression equal to 150°:
((n - 2)180) / n = 150

Multiply both sides by n:
180(n - 2) = 150n

Distribute 180:
180n - 360 = 150n

Subtract 150n from both sides:
30n - 360 = 0

Add 360 to both sides:
30n = 360

Divide by 30:
n = 12

Therefore, the regular polygon has 12 sides.