If the sum of the interior angles of a polygon is two times the sum of its exterior angles, then the number of sides of the polygon is

Options

A. 5
B. 6
C. 7
D. 8

Answer

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

### Step-by-Step Solution:

1. **Understanding the Sum of Angles**:
- The sum of the interior angles \( S_i \) of a polygon with \( n \) sides is given by the formula:
\[ S_i = 180(n - 2) \]
- The sum of the exterior angles \( S_e \) of any polygon is always:
\[ S_e = 360 \]

2. **Setting Up the Equation**:
- According to the problem, the sum of the interior angles is twice the sum of the exterior angles:
\[ S_i = 2 \times S_e \]
- Substituting the formulas we have:
\[ 180(n - 2) = 2 \times 360 \]

3. **Simplifying the Equation**:
- Calculate \( 2 \times 360 \):
\[ 2 \times 360 = 720 \]
- Now, our equation becomes:
\[ 180(n - 2) = 720 \]

4. **Dividing Both Sides by 180**:
- To isolate \( n - 2 \), divide both sides by 180:
\[ n - 2 = \frac{720}{180} \]
- Simplifying the right side:
\[ n - 2 = 4 \]

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

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

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