A regular polygon has exterior angles each measuring 15 degrees. How many sides does the polygon have?
The measure of each exterior angle in a regular $n$-gon is $360/n$ degrees.  Setting this expression equal to 15, we find $n=\boxed{24}$.
24
Level 2
Geometry
Problem: A regular polygon has exterior angles each measuring 15 degrees. How many sides does the polygon have?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of sides in a regular polygon based on the measure of its exterior angles, we need to recall that the sum of all exterior angles of any polygon is always 360 degrees. Each exterior angle of a regular polygon is equal, so we can find the number of sides by dividing the total sum of the exterior angles by the measure of one exterior angle.

Given that each exterior angle measures 15 degrees, we can set up the equation:

Number of sides = Total sum of exterior angles / Measure of one exterior angle

Substituting the known values:

Number of sides = 360 degrees / 15 degrees

Now, performing the division:

Number of sides = 24

Thus, the polygon has 24 sides.<|END_OF_LATENT|> The final answer is $24$.