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Find   x and y given l is parallel to m (need specific answer with reasons)

To solve for \( x \) and \( y \), given that lines \( l \) and \( m \) are parallel, we will use properties of parallel lines and angles formed by transversals.

### Step-by-Step Solution:

#### 1. **Using the Corresponding Angles Theorem:**
   Since \( l \parallel m \), corresponding angles formed by the transversal are congruent.

   - The angle labeled \( 70^\circ \) at the bottom left of line \( m \) corresponds to \( y \) (the angle on line \( l \)) since these two angles are in the same relative position (corresponding angles).
   - Therefore, we have:
     \[
     y = 70^\circ
     \]

#### 2. **Using the Interior Angles on the Same Side of the Transversal:**
   The sum of interior angles on the same side of the transversal is \( 180^\circ \) (co-interior angles).

   - The angles \( x \) and \( 110^\circ \) are interior angles on the same side of the transversal between \( l \) and \( m \).
   - Therefore, their sum must be \( 180^\circ \):
     \[
     x + 110^\circ = 180^\circ
     \]
   - Solving for \( x \):
     \[
     x = 180^\circ - 110^\circ = 70^\circ
     \]

### Final Answer:
- \( x = 70^\circ \)
- \( y = 70^\circ \)

Would you like further clarifications or more details on this? 

Here are five related questions to think about:
1. What are alternate interior angles, and how do they apply to parallel lines?
2. How does the corresponding angles theorem help in proving lines are parallel?
3. If another angle was added, how would you calculate it based on the current setup?
4. Can parallel lines have any angles that do not sum to 180 degrees when crossed by a transversal?
5. How can you verify parallelism using only angles and no measurements?

**Tip**: Always look for patterns like corresponding and alternate angles when dealing with parallel lines and transversals!

Learn how to solve for the angles x and y when given two parallel lines l and m intersected by a transversal. This problem utilizes the Corresponding Angles Theorem and the Co-Interior Angles Theorem. Suitable for students in Grades 8-10.

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