If a regular polygon has 5 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

Options

A. `60^@`
B. `36^@`
C. `90^@`
D. `100^@`

Answer

To solve the problem, we need to find the measures of the interior and exterior angles of a regular polygon with 5 sides (a pentagon) and then determine the difference between the two angles.

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

For a polygon with 5 sides:
\[ \text{Interior angle} = \frac{(5 - 2) \times 180}{5} \]
\[ = \frac{3 \times 180}{5} \]
\[ = \frac{540}{5} = 108 \text{ degrees} \]

### Step 2: Calculate the measure of the exterior angle
The formula for the measure of an exterior angle of a regular polygon is:
\[ \text{Exterior angle} = \frac{360}{n} \]

For a polygon with 5 sides:
\[ \text{Exterior angle} = \frac{360}{5} \]
\[ = 72 \text{ degrees} \]

### Step 3: Find the difference between the interior and exterior angles
Now, we need to find how much greater the interior angle is than the exterior angle:
\[ \text{Difference} = \text{Interior angle} - \text{Exterior angle} \]
\[ = 108 - 72 \]
\[ = 36 \text{ degrees} \]

### Final Answer
The measure of the interior angle is greater than the measure of the exterior angle by **36 degrees**.

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