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To solve this problem, we need to analyze the angles labeled in the irregular polygon. Here is the approach:

### Step-by-Step Explanation:
1. **Sum of interior angles of a polygon:**
   For a polygon with \(n\) sides (or \(n\) angles), the sum of the interior angles is given by:
   \[
   \text{Sum of interior angles} = (n - 2) \times 180^\circ
   \]
   Since there are **6 angles** (a, b, c, d, e, f), this polygon has 6 sides. Therefore:
   \[
   \text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
   \]

2. **Using the given sum of five angles:**
   The problem states:
   \[
   a + b + c + d + e = 576^\circ
   \]
   Since the total sum of all the angles is \(720^\circ\), we can find the missing angle \(f\) by subtracting the sum of the given angles from 720°:
   \[
   f = 720^\circ - 576^\circ = 144^\circ
   \]

### Final Answer:
\[
\boxed{f = 144^\circ}
\]

Would you like a more detailed breakdown or have further questions?

Here are 5 related questions for further exploration:
1. How do we derive the formula \((n - 2) \times 180^\circ\) for the sum of polygon angles?
2. What happens to the sum of angles if the polygon is concave?
3. Can the angles in a polygon ever sum to more than \(720^\circ\)?
4. How does the sum of exterior angles differ from interior angles?
5. If a polygon has all equal angles, what kind of polygon is it?

**Tip:** For irregular polygons, always ensure the given interior angles are consistent with the formula for sum of angles!

If a + b + c + d + e = 576°, find the value of angle f.

Learn how to find the missing angle in a 6-sided polygon where the sum of the other five angles is given as 576°. This solution explores the interior angle sum theorem and provides a detailed step-by-step guide suitable for students in Grades 6-9.

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