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In the given figure, if AB is parallel to CD, then the values of X and Y, respectively, are.

Let's analyze the figure to determine the values of angles \( x \) and \( y \).

### Step 1: Analyze the given information
- \( AB \) is parallel to \( CD \).
- \( \angle CAB \) is a right angle (90°).
- \( \angle ACD = 150^\circ \).
- \( \angle ABC = y \) and \( \angle DBC = x \).

### Step 2: Calculate the angle \( x \)
Given that \( AB \parallel CD \), the angles \( \angle CAB \) and \( \angle ACD \) are supplementary angles. Therefore, we have:
\[
x = 180^\circ - 150^\circ = 30^\circ
\]

### Step 3: Calculate the angle \( y \)
In the triangle \( ABC \), the sum of the angles must be \( 180^\circ \). So, using the angles in \( \triangle ABC \):
\[
\angle CAB + \angle ABC + \angle ACB = 180^\circ
\]
Substituting the values:
\[
90^\circ + y + 30^\circ = 180^\circ
\]
\[
y = 180^\circ - 120^\circ = 60^\circ
\]

### Final Answer:
- \( x = 30^\circ \)
- \( y = 60^\circ \)

Would you like a detailed explanation or have any further questions?

### Related Questions:
1. How would the angle \( y \) change if \( AB \) were not parallel to \( CD \)?
2. Can you explain how the properties of parallel lines were used to find \( x \)?
3. What would happen if \( \angle ACD \) was given as 120° instead of 150°?
4. How do you calculate angles in a triangle when two sides are known to be parallel?
5. How does the concept of supplementary angles apply to other geometric figures?

### Tip:
When working with parallel lines, always remember that corresponding and alternate interior angles are key to solving for unknown angles.

Explore how to solve for angles when lines are parallel and in triangles. Understand the properties of parallel lines and how they relate to angle calculations in geometric figures. Suitable for students in Grades 9-12.

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