Questions: If the interior angle of a regular polygon measures 108°, how many sides does the polygon have

To determine the number of sides of a regular polygon given that its interior angle measures \(108^\circ\), we can use the formula for the interior angle of a regular polygon:

\[ \text{Interior angle} = \frac{(n-2) \times 180^\circ}{n} \]

where \(n\) is the number of sides of the polygon. We are given that the interior angle is \(108^\circ\), so we set up the equation:

\[ 108 = \frac{(n-2) \times 180}{n} \]

To solve for \(n\), we first multiply both sides by \(n\) to eliminate the fraction:

\[ 108n = (n-2) \times 180 \]

Expanding the right side, we have:

\[ 108n = 180n - 360 \]

Next, we rearrange the equation to isolate terms involving \(n\) on one side:

\[ 180n - 108n = 360 \]

Simplifying, we get:

\[ 72n = 360 \]

Now, divide both sides by 72 to solve for \(n\):

\[ n = \frac{360}{72} = 5 \]

Therefore, the polygon has 5 sides.

In summary, the polygon is a regular pentagon, as it has 5 sides.