What is the sum of the measures of all the interior angles of a regular polygon of 9 sides?

Options

A. 1260
B. 1440
C. 1800
D. 2340

Explanation

To find the sum of the measures of all the interior angles of a regular polygon with 9 sides, we can use the formula for the sum of the interior angles of a polygon, which is:

\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution:

1. **Identify the number of sides (n)**:
- For our polygon, \( n = 9 \).

2. **Substitute the value of n into the formula**:
- We substitute \( n \) into the formula:
\[ \text{Sum of interior angles} = (9 - 2) \times 180^\circ \]

3. **Perform the subtraction**:
- Calculate \( 9 - 2 \):
\[ 9 - 2 = 7 \]

4. **Multiply by 180 degrees**:
- Now multiply the result by 180:
\[ 7 \times 180^\circ = 1260^\circ \]

5. **Conclusion**:
- Therefore, the sum of the measures of all the interior angles of a regular polygon with 9 sides is:
\[ \text{Sum of interior angles} = 1260^\circ \]

### Final Answer:
The sum of the measures of all the interior angles of a regular polygon of 9 sides is **1260 degrees**.

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