A line intersects two parallel lines , forming eight angles . If one of the angles has measure `a^@` , how many of the other seven angles are supplementary to it ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to analyze the situation where a line intersects two parallel lines, forming eight angles. Let's denote the angle given in the problem as \( A \).

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- When a transversal (the line) intersects two parallel lines, it creates eight angles. These angles can be categorized based on their positions relative to each other.

2. **Identifying Angles**:
- Let's label the angles formed by the intersection:
- Let angle \( A \) be one of the angles formed.
- The angles adjacent to \( A \) on the same straight line will be \( 180^\circ - A \) (since angles on a straight line sum up to \( 180^\circ \)).
- The angles opposite to \( A \) will also measure \( A \) due to the property of vertically opposite angles.

3. **Finding Supplementary Angles**:
- An angle is supplementary to another if the sum of their measures is \( 180^\circ \).
- Since one angle is \( A \), the angles that are supplementary to \( A \) will be \( 180^\circ - A \).

4. **Counting the Supplementary Angles**:
- From the configuration:
- There are two angles measuring \( 180^\circ - A \) (one adjacent to \( A \) and one opposite to it).
- Thus, there are a total of **4 angles** that are supplementary to \( A \):
- Two angles adjacent to \( A \) (one on each side of the transversal).
- Two angles opposite to \( A \) (again, one on each side of the transversal).

5. **Conclusion**:
- Therefore, the number of angles that are supplementary to the angle measuring \( A \) is **4**.

### Final Answer:
The number of angles that are supplementary to the angle measuring \( A \) is **4**.