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To find the number of sides \(n\) in a regular polygon where the measure of an interior angle is given as 108°, we can use the formula for the interior angle of a regular polygon:

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

Given that the interior angle is 108°, we substitute that value into the equation:

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

Now, let's solve for \(n\):

1. Multiply both sides by \(n\) to eliminate the denominator:
   \[
   108n = (n - 2) \times 180
   \]

2. Expand the right-hand side:
   \[
   108n = 180n - 360
   \]

3. Move all terms involving \(n\) to one side:
   \[
   180n - 108n = 360
   \]

4. Simplify:
   \[
   72n = 360
   \]

5. Solve for \(n\):
   \[
   n = \frac{360}{72} = 5
   \]

Thus, the polygon has 5 sides, meaning it is a regular pentagon.

Would you like further details or have any questions?

Here are some related questions:
1. What is the formula for the exterior angle of a regular polygon?
2. How do you calculate the sum of interior angles of any polygon?
3. Can a regular polygon have an interior angle of 150°? How many sides would it have?
4. What is the relationship between interior and exterior angles in a regular polygon?
5. If the number of sides of a polygon is doubled, how does that affect its interior angle?

**Tip:** The exterior angle of a regular polygon is always supplementary to the interior angle, and you can easily calculate the number of sides by dividing 360° by the exterior angle!

The measure of an interior angle of a regular polygon is 108°. Find the number of sides in the polygon.

Learn how to calculate the number of sides in a regular polygon with a given interior angle of 108°. This problem applies the polygon interior angle formula, suitable for students in Grades 8-10.

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