Question

The measure of an exterior angle of a regular polygon is given. Find the number of sides.

30° n=


72° n =

Answer 1

To find the number of sides \( n \) of a regular polygon given the measure of its exterior angle, you can use the formula:

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

From this formula, you can solve for \( n \):

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

Now, let's apply this formula to the given exterior angles.

1. For an exterior angle of \( 30° \):

\[
n = \frac{360°}{30°} = 12
\]

So, for the exterior angle of \( 30° \), the polygon has \( n = 12 \) sides.

2. For an exterior angle of \( 72° \):

\[
n = \frac{360°}{72°} = 5
\]

So, for the exterior angle of \( 72° \), the polygon has \( n = 5 \) sides.

### Summary:
- For \( 30° \): \( n = 12 \)
- For \( 72° \): \( n = 5 \)