Polygon Angle Sum Calculation
To find the sum of the interior angles of a polygon, we use a specific formula based on the number of sides.
Interior Angle Sum Formula
The formula for the sum of the interior angles of a polygon with n sides is:
$ \text{Sum} = (n-2) \times 180^\circ $
Applying the Formula
In this question, the polygon has 11 sides. So, we set n = 11.
- Substitute the value of n into the formula:
$ \text{Sum} = (11-2) \times 180^\circ $
- Calculate the value inside the parentheses:
$ \text{Sum} = 9 \times 180^\circ $
- Perform the multiplication:
$ \text{Sum} = 1620^\circ $
Conclusion
The sum of the interior angles of a polygon with 11 sides is $1620^\circ$. This matches Option 4.
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