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!