Eight straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. The number of parts into which these lines divide the plane, is :

Options

A. 73
B. 37
C. 17
D. 72

Answer

To solve the problem of how many parts eight straight lines divide the plane into, given that no two lines are parallel and no three lines are concurrent, we can use a standard formula for this scenario.

### Step-by-Step Solution:

1. **Identify the number of lines (n)**:
We have \( n = 8 \) lines.

2. **Use the formula**:
The formula to find the number of regions \( R \) created by \( n \) lines in the plane is given by:
\[ R(n) = \frac{n(n + 1)}{2} + 1 \]

3. **Substitute the value of n into the formula**:
Plugging in \( n = 8 \):
\[ R(8) = \frac{8(8 + 1)}{2} + 1 \]

4. **Calculate \( 8 + 1 \)**:
\[ 8 + 1 = 9 \]

5. **Multiply \( 8 \) by \( 9 \)**:
\[ 8 \times 9 = 72 \]

6. **Divide by \( 2 \)**:
\[ \frac{72}{2} = 36 \]

7. **Add \( 1 \)**:
\[ 36 + 1 = 37 \]

8. **Conclusion**:
Therefore, the number of parts into which the eight lines divide the plane is \( 37 \).

### Final Answer:
The correct option is **b) 37**.