Condier the following statement
if a transversal line cuts two parallel line then
1 Each pair of corresponding angles are equal
2 Each pair of alternalte angles are unequal
Among these true statements are

Options

A. only 1
B. only 2
C. both 1 and 2
D. neigher 1 nor 2

Answer

To solve the question, we need to analyze the statements regarding the angles formed when a transversal cuts two parallel lines.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two parallel lines, let's call them Line A and Line B.
- A transversal line, which we will call Line C, intersects both Line A and Line B.

2. **Identifying Corresponding Angles**:
- When Line C intersects Line A and Line B, it creates several angles.
- Corresponding angles are the angles that are in the same relative position at each intersection. For example, if we label the angles formed as follows:
- Angle 1 and Angle 2 are corresponding angles.
- Angle 3 and Angle 4 are corresponding angles.
- Angle 5 and Angle 6 are corresponding angles.
- Angle 7 and Angle 8 are corresponding angles.
- The property of parallel lines states that each pair of corresponding angles is equal. Therefore, we can conclude that:
- Angle 1 = Angle 2
- Angle 3 = Angle 4
- Angle 5 = Angle 6
- Angle 7 = Angle 8

3. **Identifying Alternate Angles**:
- Alternate angles are the angles that are on opposite sides of the transversal and inside the parallel lines.
- For example, Angle 5 and Angle 8 are alternate angles, and so are Angle 2 and Angle 7.
- The property of parallel lines states that each pair of alternate angles is also equal. Therefore, we can conclude that:
- Angle 5 = Angle 8
- Angle 2 = Angle 7
- Angle 1 = Angle 4
- Angle 3 = Angle 6

4. **Evaluating the Statements**:
- The first statement claims that "each pair of corresponding angles are equal." This statement is **true**.
- The second statement claims that "each pair of alternate angles are unequal." This statement is **false** because alternate angles are equal when two parallel lines are cut by a transversal.

5. **Conclusion**:
- Among the given statements, only the first statement is true. Therefore, the correct answer is that only statement 1 is true.

### Final Answer:
Only statement 1 is true.

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