The question is asking to find angles $x$ and $y$, based on the provided diagram where the angles $\angle x$ and $\angle y$ are part of a transversal cutting through two parallel lines.

Given Information:

• Parallel lines are given as $l \parallel m$, and a transversal is intersecting these parallel lines.
• $\angle x$ and $\angle y$ are the unknown angles.
• $\angle b = 110^\circ$ and $\angle d = 70^\circ$ are marked in the diagram.

Steps to Solve:

1. Identify relationships using parallel lines:

   • Since lines $l$ and $m$ are parallel, angles formed by the transversal have certain relationships like corresponding angles, alternate interior angles, and consecutive interior angles.

2. Find $x$:

   • $\angle x$ and $\angle b = 110^\circ$ form a linear pair on a straight line, which means they are supplementary.
   • $x + 110^\circ = 180^\circ$
   • $x = 180^\circ - 110^\circ = 70^\circ$

3. Find $y$:

   • $\angle y$ and $\angle d = 70^\circ$ are corresponding angles since they are on the same side of the transversal.
   • By the corresponding angles postulate: $y = 70^\circ$.

Final Answer:

• $x = 70^\circ$
• $y = 70^\circ$

Let me know if you'd like further explanation or have any questions.

Here are 5 related questions:

1. How do we identify corresponding angles in parallel lines?
2. What is the relationship between alternate interior angles in parallel lines?
3. Why are angles on a straight line supplementary?
4. How do we prove that two lines are parallel using angle relationships?
5. Can transversal lines create vertical angles, and how do we calculate those?

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