If a regular polygon has 10 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

Options

A. 120
B. 132
C. 140
D. 108

Answer

To find the difference between the measure of the interior angle and the measure of the exterior angle of a regular polygon with 10 sides, we can follow these steps:

### Step 1: Understand the formulas
The formulas for the interior and exterior angles of a regular polygon are:
- Interior angle = \(\frac{(n-2) \times 180}{n}\)
- Exterior angle = \(\frac{360}{n}\)

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

### Step 2: Substitute \(n = 10\)
Since the polygon has 10 sides, we substitute \(n\) with 10 in both formulas.

### Step 3: Calculate the interior angle
Using the formula for the interior angle:
\[ \text{Interior angle} = \frac{(10-2) \times 180}{10} = \frac{8 \times 180}{10} = \frac{1440}{10} = 144 \text{ degrees} \]

### Step 4: Calculate the exterior angle
Using the formula for the exterior angle:
\[ \text{Exterior angle} = \frac{360}{10} = 36 \text{ degrees} \]

### Step 5: Find the difference
Now, we find the difference between the interior angle and the exterior angle:
\[ \text{Difference} = \text{Interior angle} - \text{Exterior angle} = 144 - 36 = 108 \text{ degrees} \]

### Final Answer
The measure of the interior angle is greater than the measure of the exterior angle by **108 degrees**.

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