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We are asked to find the number of sides of a regular polygon whose interior angle is given as \( 165^\circ \).

### Step-by-Step Solution:

1. **Formula for the interior angle of a regular polygon:**
   The interior angle \( A \) of a regular polygon with \( n \) sides is given by the formula:
   \[
   A = \frac{(n - 2) \times 180^\circ}{n}
   \]
   where \( n \) is the number of sides.

2. **Given information:**
   \[
   A = 165^\circ
   \]
   We substitute this into the formula:
   \[
   165 = \frac{(n - 2) \times 180}{n}
   \]

3. **Solve for \( n \):**
   Multiply both sides by \( n \) to eliminate the denominator:
   \[
   165n = (n - 2) \times 180
   \]
   Expand the right-hand side:
   \[
   165n = 180n - 360
   \]
   Rearrange to isolate terms involving \( n \):
   \[
   180n - 165n = 360
   \]
   \[
   15n = 360
   \]
   Finally, solve for \( n \):
   \[
   n = \frac{360}{15} = 24
   \]

### Conclusion:
The polygon has **24 sides**.

Would you like further explanation on this solution or related details?

Here are 5 related questions for further exploration:
1. How do you calculate the exterior angle of a regular polygon?
2. Can the interior angle of a polygon be more than \(180^\circ\)?
3. How would the number of sides change if the interior angle were \(170^\circ\)?
4. What is the sum of the interior angles of a polygon with 24 sides?
5. How does the number of sides affect the shape of a regular polygon?

**Tip:** The exterior angle of any regular polygon can be found using the formula \( \text{Exterior angle} = \frac{360^\circ}{n} \), which is often useful in geometry problems.

A regular polygon has its interior angles all equal to 165°. Find the number of sides of the polygon.

Learn how to calculate the number of sides of a regular polygon given that its interior angles are 165°. This step-by-step solution uses the formula for the interior angles of a polygon, suitable for Grades 8-10.

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