In Fig. 52. `A B||C Ddot` Determine `/_a`

Options

A. `38^@`
B. `93^@`
C. `55^@`
D. `83^@`

Answer

To determine angle A in the given figure where AB is parallel to CD, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parallel Lines and Transversal**:
We have two parallel lines, AB and CD, and a transversal line (let's call it line L) that intersects both lines.

2. **Label the Angles**:
Let's denote the angles formed by the transversal with the parallel lines. Assume angle 1 is formed at line AB and angle 2 is formed at line CD.

3. **Use the Given Angles**:
From the problem, we know that:
- Angle 1 = 55 degrees
- Angle 2 = 38 degrees

4. **Identify the Relationship Between Angles**:
Since AB is parallel to CD and line L is a transversal, angle 1 and angle 2 are alternate interior angles. According to the properties of parallel lines, alternate interior angles are equal.

5. **Calculate Angle A**:
Angle A can be found by adding angle 1 and angle 2:
\[ \text{Angle A} = \text{Angle 1} + \text{Angle 2} = 55^\circ + 38^\circ \]
Now, perform the addition:
\[ 55 + 38 = 93^\circ \]

6. **Conclusion**:
Therefore, angle A is equal to 93 degrees.

### Final Answer:
Angle A = 93 degrees.

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