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We are asked to find the number of sides in an irregular polygon where one exterior angle is \(120^\circ\), and all other exterior angles are \(12^\circ\).

### Key Concepts:
1. **Sum of exterior angles in a polygon**:
   The sum of the exterior angles of any polygon is always \(360^\circ\), regardless of whether it is regular or irregular.

2. **Approach**:
   - Let \(n\) be the total number of sides of the polygon.
   - We know that one exterior angle is \(120^\circ\), and the remaining \((n-1)\) exterior angles are each \(12^\circ\).

### Step-by-step Solution:
- The sum of all exterior angles is given by:
  \[
  120^\circ + (n-1) \times 12^\circ = 360^\circ
  \]
  
- Simplifying the equation:
  \[
  120^\circ + 12^\circ(n - 1) = 360^\circ
  \]
  \[
  120^\circ + 12^\circ n - 12^\circ = 360^\circ
  \]
  \[
  12^\circ n + 108^\circ = 360^\circ
  \]
  \[
  12^\circ n = 360^\circ - 108^\circ
  \]
  \[
  12^\circ n = 252^\circ
  \]
  \[
  n = \frac{252^\circ}{12^\circ} = 21
  \]

### Final Answer:
The polygon has **21 sides**.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. What is the relationship between exterior angles and the number of sides in a polygon?
2. How would the formula change if all the angles were equal?
3. Can you explain how the sum of exterior angles is always \(360^\circ\)?
4. What is the formula for finding the number of sides in a regular polygon if all exterior angles are given?
5. How does the irregularity of the polygon affect the calculation?

**Tip**: For any polygon, the sum of exterior angles is always \(360^\circ\), whether the polygon is regular or irregular!

Find the number of sides in an irregular polygon with one exterior angle of 120° and all others 12°.

Learn how to determine the number of sides in an irregular polygon with one exterior angle of 120° and all others measuring 12°. This problem demonstrates key geometry concepts such as the sum of exterior angles and polygon properties. Suitable for high school students in Grades 9-12.

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