If each interior angle of a regular polygon is 3 times its exterior angle, the number of sides of the polygon is :

Options

A. 4
B. 5
C. 6
D. 8

Answer

To solve the problem, we need to find the number of sides of a regular polygon where each interior angle is three times its exterior angle.

### Step-by-Step Solution:

1. **Understanding the Relationship Between Interior and Exterior Angles**:
- Let the exterior angle be denoted as \( E \).
- According to the problem, the interior angle \( I \) is three times the exterior angle:
\[ I = 3E \]

2. **Using the Relationship Between Interior and Exterior Angles**:
- We know that the sum of the interior angle and the exterior angle is \( 180^\circ \):
\[ I + E = 180^\circ \]
- Substituting \( I = 3E \) into the equation gives:
\[ 3E + E = 180^\circ \]
- This simplifies to:
\[ 4E = 180^\circ \]

3. **Solving for the Exterior Angle**:
- Dividing both sides by 4:
\[ E = \frac{180^\circ}{4} = 45^\circ \]

4. **Finding the Number of Sides of the Polygon**:
- The formula for the exterior angle of a regular polygon with \( n \) sides is:
\[ E = \frac{360^\circ}{n} \]
- Setting this equal to the exterior angle we found:
\[ \frac{360^\circ}{n} = 45^\circ \]
- Cross-multiplying gives:
\[ 360 = 45n \]
- Dividing both sides by 45:
\[ n = \frac{360}{45} = 8 \]

5. **Conclusion**:
- Therefore, the number of sides of the polygon is \( n = 8 \).

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