https://file.aiquickdraw.com/mathbot/file/1729010869217bcaos6yo.jpg

To solve for the angle \(y\), let’s follow these steps.

### Step-by-step working:

1. **Identify corresponding angles:**  
   Since \(AB \parallel CD\) and \(EF\) is a transversal, the angle at \(B\) (which is \(2x + 15^\circ\)) corresponds to the angle at \(D\) (which is \(3x - 5^\circ\)).  
   **Corresponding angles are equal**:  
   \[
   2x + 15^\circ = 3x - 5^\circ
   \]

2. **Solve for \(x\):**  
   Rearranging the equation:  
   \[
   15^\circ + 5^\circ = 3x - 2x
   \]
   \[
   20^\circ = x
   \]

3. **Substitute \(x = 20^\circ\) into the expression for angle \(y\):**  
   The expression for angle \(y\) is given as:
   \[
   y = 3x - 5^\circ
   \]
   Substituting \(x = 20^\circ\):
   \[
   y = 3(20^\circ) - 5^\circ = 60^\circ - 5^\circ = 55^\circ
   \]

### Final Answer:
\[
y = 55^\circ
\]

Would you like me to explain any step further or do another related problem?

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Here are 5 questions related to the problem for further exploration:
1. What are corresponding angles, and why are they equal when two lines are parallel?
2. How would the solution change if the lines were not parallel?
3. Can you identify alternate interior angles in this figure? Are they equal?
4. What is the sum of the interior angles on the same side of a transversal?
5. How does this problem relate to real-world parallel lines, such as those in bridges or railway tracks?

**Tip:** Always look for corresponding, alternate, or co-interior angles when working with parallel lines.

AB, CD, and EF are straight lines. AB is parallel to CD. Work out the size of angle y, where angle B is 2x + 15° and angle D is 3x - 5°.

This problem demonstrates how to find the size of an angle in a figure involving parallel lines and a transversal. By using the Corresponding Angles Theorem, students solve for angle y. The problem is suitable for students in Grade 8-10 and covers key concepts like algebraic manipulation and angle relationships in parallel lines.

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