The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.

Options

A. `8`
B. `7`
C. `5`
D. `9`

Answer

To solve the problem, we need to find the number of sides \( n \) of a regular polygon given that the sum of its interior angles is twice the sum of its exterior angles.

### Step-by-Step Solution:

1. **Understand the formulas**:
- The sum of the interior angles of a regular polygon is given by the formula:
\[ \text{Sum of interior angles} = 180(n - 2) \]
- The sum of the exterior angles of any polygon is always:
\[ \text{Sum of exterior angles} = 360 \]

2. **Set up the equation**:
- According to the problem, the sum of the interior angles is twice the sum of the exterior angles. Therefore, we can write the equation:
\[ 180(n - 2) = 2 \times 360 \]

3. **Simplify the equation**:
- Calculate \( 2 \times 360 \):
\[ 2 \times 360 = 720 \]
- Now, substitute this back into the equation:
\[ 180(n - 2) = 720 \]

4. **Divide both sides by 180**:
- To isolate \( n - 2 \), divide both sides by 180:
\[ n - 2 = \frac{720}{180} \]

5. **Calculate the right side**:
- Simplifying \( \frac{720}{180} \):
\[ \frac{720}{180} = 4 \]
- So, we have:
\[ n - 2 = 4 \]

6. **Solve for \( n \)**:
- Add 2 to both sides to find \( n \):
\[ n = 4 + 2 = 6 \]

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

### Final Answer:
The number of sides of the polygon is **6**.