Find each interior of a regular pentagon.

Options

A. `108^(@)`
B. `105^(@)`
C. `103^(@)`
D. `101^(@)`

Answer

To find each interior angle of a regular pentagon, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Sides**:
A regular pentagon has 5 sides.

2. **Calculate the Exterior Angle**:
The formula for the exterior angle of a regular polygon is given by:
\[ \text{Exterior Angle} = \frac{360^\circ}{n} \]
where \( n \) is the number of sides. For a pentagon, \( n = 5 \):
\[ \text{Exterior Angle} = \frac{360^\circ}{5} = 72^\circ \]

3. **Calculate the Interior Angle**:
The interior angle can be found using the relationship between interior and exterior angles:
\[ \text{Interior Angle} = 180^\circ - \text{Exterior Angle} \]
Substituting the value of the exterior angle:
\[ \text{Interior Angle} = 180^\circ - 72^\circ = 108^\circ \]

4. **Conclusion**:
Each interior angle of a regular pentagon is \( 108^\circ \).

### Final Answer:
Each interior angle of a regular pentagon is \( 108^\circ \).

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