A regular polygon is inscribed in a circle. If a side subtends an angle of `45^(@)` at the centre. What is the number of sides of the polygon ?

Options

A. 6
B. 5
C. 10
D. 8

Answer

To find the number of sides of a regular polygon inscribed in a circle, given that a side subtends an angle of 45 degrees at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the number of sides and the angle subtended**:
For a regular polygon with \( n \) sides, the angle subtended at the center by one side is given by the formula:
\[ \text{Angle at center} = \frac{360^\circ}{n} \]

2. **Set up the equation**:
According to the problem, the angle subtended at the center by one side is 45 degrees. Therefore, we can set up the equation:
\[ \frac{360^\circ}{n} = 45^\circ \]

3. **Cross-multiply to solve for \( n \)**:
To eliminate the fraction, we can cross-multiply:
\[ 360^\circ = 45^\circ \times n \]

4. **Isolate \( n \)**:
Now, divide both sides by 45 degrees to solve for \( n \):
\[ n = \frac{360^\circ}{45^\circ} \]

5. **Calculate \( n \)**:
Performing the division:
\[ n = 8 \]

6. **Conclusion**:
The number of sides of the polygon is \( n = 8 \).

### Final Answer:
The number of sides of the polygon is **8**.