Select the correct answer.

Transversal C⁢D⟷ cuts parallel lines P⁢Q⟷ and R⁢S⟷ at points *X* and *Y* as shown in the diagram. If m∠C⁢X⁢P = 106.02°, what is m∠S⁢Y⁢D?

 **A.** 

73.98°

 **B.** 

90°

 **C.** 

106.02°

To solve this problem, we need to use the properties of parallel lines cut by a transversal.

Given:
- \( \overleftrightarrow{CD} \) is a transversal cutting the parallel lines \( \overleftrightarrow{PQ} \) and \( \overleftrightarrow{RS} \) at points \( X \) and \( Y \), respectively.
- \( m\angle CXP = 106.02^\circ \).

We want to find \( m\angle SYD \).

### Step-by-Step Solution:

1. **Identify the Type of Angles:**
   - When a transversal cuts two parallel lines, it forms several pairs of angles: corresponding angles, alternate interior angles, and co-interior (consecutive) angles.
   - Since \( m\angle CXP = 106.02^\circ \), this angle is an **exterior angle** formed between the transversal \( \overleftrightarrow{CD} \) and line \( \overleftrightarrow{PQ} \).

2. **Relationship Between Alternate Interior Angles:**
   - Alternate interior angles are equal when a transversal cuts two parallel lines.
   - \( \angle CXP \) and \( \angle SYD \) are **alternate interior angles** formed by transversal \( \overleftrightarrow{CD} \) cutting parallel lines \( \overleftrightarrow{PQ} \) and \( \overleftrightarrow{RS} \).

3. **Apply the Angle Property:**
   - Since alternate interior angles are equal, we have:
   \[
   m\angle SYD = m\angle CXP = 106.02^\circ.
   \]

### Conclusion:
The measure of \( m\angle SYD \) is \( 106.02^\circ \).

### Correct Answer: **C. 106.02°**

Would you like more details or have any questions? Here are some related questions that might help further your understanding:

1. What are corresponding angles when a transversal cuts parallel lines?
2. How do co-interior angles relate when a transversal cuts parallel lines?
3. What is the sum of consecutive interior angles formed by a transversal?
4. How do you determine if two lines are parallel using angles formed by a transversal?
5. What is the difference between alternate interior and alternate exterior angles?

**Tip:** When dealing with angles formed by a transversal cutting parallel lines, always look for alternate interior, corresponding, and co-interior angle relationships to solve the problem efficiently.

Explore how to solve angles formed by a transversal cutting parallel lines with a detailed step-by-step solution. This problem involves the Alternate Interior Angles Theorem and is suitable for students in Grades 7-9.

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