What is the measure of an interior angle of a regular polygon of 12 sides?

Options

A. 150
B. 156
C. 144
D. 160

Answer

To find the measure of an interior angle of a regular polygon with 12 sides, we can use the formula for the interior angle of a regular polygon:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \]

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

### Step-by-Step Solution:

1. **Identify the number of sides (n)**:
- For this problem, \( n = 12 \) (since the polygon has 12 sides).

2. **Substitute n into the formula**:
- Plugging in the value of \( n \):
\[ \text{Interior Angle} = \frac{(12 - 2) \times 180}{12} \]

3. **Simplify the expression**:
- Calculate \( 12 - 2 \):
\[ 12 - 2 = 10 \]
- Now substitute back into the formula:
\[ \text{Interior Angle} = \frac{10 \times 180}{12} \]

4. **Perform the multiplication**:
- Calculate \( 10 \times 180 \):
\[ 10 \times 180 = 1800 \]

5. **Divide by the number of sides**:
- Now divide \( 1800 \) by \( 12 \):
\[ \text{Interior Angle} = \frac{1800}{12} = 150 \]

Thus, the measure of an interior angle of a regular polygon with 12 sides is \( 150^\circ \).

### Final Answer:
The measure of an interior angle of a regular polygon of 12 sides is \( 150^\circ \).