The number of sides of a regular polygon whose interior angles are each `150^(@)` is :

Options

A. 15
B. 13
C. 12
D. 14

Answer

To find the number of sides of a regular polygon whose interior angles are each \(150^\circ\), we can follow these steps:

### Step 1: Find the Exterior Angle
The exterior angle of a polygon can be found using the relationship between interior and exterior angles. The sum of the interior angle and the exterior angle is \(180^\circ\).

\[ \text{Exterior Angle} = 180^\circ - \text{Interior Angle} \]

Substituting the given interior angle:

\[ \text{Exterior Angle} = 180^\circ - 150^\circ = 30^\circ \]

### Step 2: Use the Formula for the Number of Sides
The sum of all exterior angles of any polygon is always \(360^\circ\). To find the number of sides \(n\) of the polygon, we use the formula:

\[ n = \frac{\text{Sum of Exterior Angles}}{\text{One Exterior Angle}} \]

Substituting the values we have:

\[ n = \frac{360^\circ}{30^\circ} \]

### Step 3: Calculate the Number of Sides
Now, we perform the division:

\[ n = \frac{360}{30} = 12 \]

Thus, the number of sides of the polygon is \(12\).

### Conclusion
The number of sides of a regular polygon whose interior angles are each \(150^\circ\) is \(12\).

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