The number of sides of a regular polygon whose interior angles are each `168^(@)` is:

Options

A. 20
B. 30
C. 15
D. 31

Answer

To find the number of sides of a regular polygon whose interior angles are each \(168^\circ\), we can follow these steps:

### Step 1: Understand the relationship between interior and exterior angles
The interior angle of a polygon and its corresponding exterior angle are related by the formula:
\[ \text{Exterior Angle} = 180^\circ - \text{Interior Angle} \]

### Step 2: Calculate the exterior angle
Given that the interior angle is \(168^\circ\):
\[ \text{Exterior Angle} = 180^\circ - 168^\circ = 12^\circ \]

### Step 3: Use the formula for the number of sides
The formula to find the number of sides \(n\) of a regular polygon based on its exterior angle is:
\[ n = \frac{360^\circ}{\text{Exterior Angle}} \]

### Step 4: Substitute the exterior angle into the formula
Substituting the exterior angle we calculated:
\[ n = \frac{360^\circ}{12^\circ} \]

### Step 5: Perform the division
Calculating the above expression:
\[ n = 30 \]

### Conclusion
The number of sides of the regular polygon is \(30\).

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