If the sum of Interior angles of a regular polygon is equal to two times the sum of exterior angles of that polygon, then the number of sides of that 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 regular polygon given that the sum of its interior angles is equal to two times the sum of its exterior angles.

### Step-by-Step Solution:

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

2. **Setting up the equation**:
- According to the problem, the sum of the interior angles is equal to two times the sum of the exterior angles:
\[ (n - 2) \times 180^\circ = 2 \times 360^\circ \]

3. **Simplifying the right side**:
- Calculate \( 2 \times 360^\circ \):
\[ 2 \times 360^\circ = 720^\circ \]
- Thus, we can rewrite the equation as:
\[ (n - 2) \times 180^\circ = 720^\circ \]

4. **Dividing both sides by 180**:
- To isolate \( n - 2 \), divide both sides by \( 180^\circ \):
\[ n - 2 = \frac{720^\circ}{180^\circ} \]
- Calculate \( \frac{720}{180} \):
\[ \frac{720}{180} = 4 \]
- So, we have:
\[ n - 2 = 4 \]

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

6. **Conclusion**:
- Therefore, the number of sides of the polygon is \( 6 \).

### Final Answer:
The number of sides of the polygon is \( 6 \).

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