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The problem asks for the number of sides of an irregular polygon, where one exterior angle is \(100^\circ\) and all the other exterior angles are \(13^\circ\).

### Step 1: Sum of Exterior Angles
The sum of the exterior angles of any polygon is always \(360^\circ\), regardless of the number of sides.

### Step 2: Set Up the Equation
Let the total number of sides be \(n\). Since one of the exterior angles is \(100^\circ\), the remaining \(n - 1\) angles are each \(13^\circ\).

Thus, we can write the equation for the sum of the exterior angles:
\[
100^\circ + 13^\circ(n - 1) = 360^\circ
\]

### Step 3: Solve for \(n\)
Now, simplify and solve for \(n\):

\[
100 + 13(n - 1) = 360
\]

\[
100 + 13n - 13 = 360
\]

\[
13n + 87 = 360
\]

\[
13n = 360 - 87
\]

\[
13n = 273
\]

\[
n = \frac{273}{13}
\]

\[
n = 21
\]

### Conclusion
The polygon has **21 sides**.

Would you like further clarification, or more details? Here are some related questions to explore:

1. How can we verify that the sum of exterior angles is always 360°?
2. What is the formula for calculating the exterior angle of a regular polygon?
3. How do we handle the case where more than one exterior angle differs from the others?
4. Can an irregular polygon have more than two different exterior angles?
5. How would this approach change if the polygon were regular?

**Tip:** For any polygon, the sum of the exterior angles is always 360°, no matter how irregular or complex the shape is.

An irregular polygon has one exterior angle 100° and all others 13°. How many sides does it have?

Learn how to find the number of sides in an irregular polygon with one exterior angle of 100° and the others 13°. Explore key algebraic steps and the exterior angle sum theorem. Suitable for students in Grades 8-10.

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