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

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

• A. 120 degrees
• B. 135 degrees
• C. 150 degrees
• D. 160 degrees

Answer: (C)

To determine the measure of an interior angle of a regular polygon, you can use the formula: \[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \] where \( n \) is the number of sides of the polygon. In this case, the polygon has 12 sides (a dodecagon), so \( n = 12 \). Plugging in the values: \[ \text{Interior Angle} = \frac{(12 - 2) \times 180}{12} \] Calculating this step-by-step: 1. Calculate \( n - 2 \): \[ 12 - 2 = 10 \] 2. Multiply by 180: \[ 10 \times 180 = 1800 \] 3. Divide by \( n \): \[ \frac{1800}{12} = 150 \] Thus, each interior angle of a regular dodecagon measures 150 degrees. This calculation confirms that the interior angle of a regular polygon with 12 sides is indeed 150 degrees.

To determine the measure of an interior angle of a regular polygon, you can use the formula:

[

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

]

where ( n ) is the number of sides of the polygon. In this case, the polygon has 12 sides (a dodecagon), so ( n = 12 ).

Plugging in the values:

[

\text{Interior Angle} = \frac{(12 - 2) \times 180}{12}

]

Calculating this step-by-step:

1. Calculate ( n - 2 ):

[

12 - 2 = 10

]

2. Multiply by 180:

[

10 \times 180 = 1800

]

3. Divide by ( n ):

[

\frac{1800}{12} = 150

]

Thus, each interior angle of a regular dodecagon measures 150 degrees.

This calculation confirms that the interior angle of a regular polygon with 12 sides is indeed 150 degrees.