A regular polygon is inscribed in a circle. If a side subtends an angle of `30^(@)` at the centre, what is the number of its sides ?

Options

A. 10
B. 8
C. 6
D. 12

Answer

To find the number of sides of a regular polygon inscribed in a circle, where a side subtends an angle of 30 degrees at the center, we can follow these steps:

### Step 1: Understand the relationship between the angle and the number of sides
In a regular polygon, the angle subtended by each side at the center of the circle can be calculated using the formula:
\[ \text{Angle at center} = \frac{360^\circ}{n} \]
where \( n \) is the number of sides of the polygon.

### Step 2: Set up the equation
Given that the angle subtended by one side at the center is \( 30^\circ \), we can set up the equation:
\[ 30 = \frac{360}{n} \]

### Step 3: Solve for \( n \)
To find \( n \), we can rearrange the equation:
\[ n = \frac{360}{30} \]

### Step 4: Perform the division
Now, calculate \( n \):
\[ n = \frac{360}{30} = 12 \]

### Step 5: Conclusion
Thus, the number of sides of the regular polygon is \( 12 \).