What is the sum of all the angles of a 9 pointed star `("i.e., "angle1 + angle2 + angle3 + ….. angle8 + angle9)`

Options

A. `909^(@)`
B. `900^(@)`
C. `720^(@)`
D. `540^(@)`

Answer

To find the sum of all the angles of a 9-pointed star, we can follow these steps:

### Step 1: Identify the formula for the sum of angles in a star
The formula for the sum of the angles of an n-pointed star is given by:
\[ \text{Sum of angles} = (n - 4) \times 180 \]
where \( n \) is the number of points in the star.

### Step 2: Substitute the value of \( n \)
In this case, we have a 9-pointed star, so we substitute \( n = 9 \) into the formula:
\[ \text{Sum of angles} = (9 - 4) \times 180 \]

### Step 3: Perform the subtraction
Calculate \( 9 - 4 \):
\[ 9 - 4 = 5 \]

### Step 4: Multiply by 180
Now, multiply the result by 180:
\[ \text{Sum of angles} = 5 \times 180 \]

### Step 5: Calculate the final result
Now, calculate \( 5 \times 180 \):
\[ 5 \times 180 = 900 \]

### Final Answer
Thus, the sum of all the angles of a 9-pointed star is:
\[ \text{Sum of angles} = 900 \]

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