Find the measure of each interior angle of a regular polygon of 15 sides:

Options

A. A)`106^@`
B. B)`156^@`
C. C)`206^@`
D. D)`256^@`

Answer

To find the measure of each interior angle of a regular polygon with 15 sides, we can follow these steps:

### Step 1: Understand the formula for the sum of interior angles
The sum of the interior angles of a polygon can be calculated using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides in the polygon.

### Step 2: Substitute the number of sides
In this case, the polygon has 15 sides, so we substitute \( n = 15 \) into the formula:
\[ \text{Sum of interior angles} = (15 - 2) \times 180^\circ \]

### Step 3: Calculate the sum of interior angles
Now, calculate \( 15 - 2 \):
\[ 15 - 2 = 13 \]
Now, multiply by 180 degrees:
\[ \text{Sum of interior angles} = 13 \times 180^\circ = 2340^\circ \]

### Step 4: Find the measure of each interior angle
To find the measure of each interior angle in a regular polygon, we divide the sum of the interior angles by the number of sides:
\[ \text{Each interior angle} = \frac{\text{Sum of interior angles}}{n} = \frac{2340^\circ}{15} \]

### Step 5: Perform the division
Now, divide 2340 by 15:
\[ \text{Each interior angle} = 156^\circ \]

### Conclusion
Thus, the measure of each interior angle of a regular polygon with 15 sides is:
\[ \boxed{156^\circ} \]