What is the measure of an interior angle of a regular polygon of 8 sides?

Options

A. 140
B. `144`
C. `135`
D. `150`

Answer

To find the measure of an interior angle of a regular polygon with 8 sides, we can follow these steps:

### Step 1: Identify the formula for the interior angle of a regular polygon
The formula to find the measure of each interior angle of a regular polygon is given by:
\[ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} \]
where \( n \) is the number of sides of the polygon.

### Step 2: Substitute the number of sides into the formula
For a polygon with 8 sides, we substitute \( n = 8 \) into the formula:
\[ \text{Interior Angle} = \frac{(8 - 2) \times 180^\circ}{8} \]

### Step 3: Simplify the expression
Now, simplify the expression:
\[ \text{Interior Angle} = \frac{6 \times 180^\circ}{8} \]

### Step 4: Calculate \( 6 \times 180^\circ \)
Calculate \( 6 \times 180^\circ \):
\[ 6 \times 180^\circ = 1080^\circ \]

### Step 5: Divide by 8
Now, divide \( 1080^\circ \) by 8:
\[ \text{Interior Angle} = \frac{1080^\circ}{8} = 135^\circ \]

### Conclusion
The measure of each interior angle of a regular polygon with 8 sides is \( 135^\circ \).

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