A regular polygon has sides of length 5 units and an exterior angle of 120 degrees. What is the perimeter of the polygon, in units?
If an exterior angle has measure $120$ degrees, an interior angle has measure $60$ degrees.  A regular polygon with $60$ degree angles must be an equilateral triangle, so the perimeter is $3(5)=\boxed{15}$ units.
15
Level 5
Prealgebra
Problem: A regular polygon has sides of length 5 units and an exterior angle of 120 degrees. What is the perimeter of the polygon, in units?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the perimeter of the polygon, we first need to determine the number of sides it has. The relationship between the exterior angle and the number of sides \( n \) of a regular polygon is given by the formula:

\[
\text{Exterior angle} = \frac{360}{n}
\]

Given that the exterior angle is 120 degrees, we can set up the equation:

\[
120 = \frac{360}{n}
\]

To solve for \( n \), we rearrange the equation:

\[
n = \frac{360}{120}
\]

Calculating this gives:

\[
n = 3
\]

This indicates that the polygon is a triangle, as it has 3 sides. Next, we calculate the perimeter of the polygon. The perimeter \( P \) of a regular polygon is given by the formula:

\[
P = n \times \text{side length}
\]

Substituting the values we have:

\[
P = 3 \times 5
\]

Calculating this yields:

\[
P = 15
\]

Thus, the perimeter of the polygon is 15 units.<|END_OF_LATENT|> The final answer is $15$.