Let's re-examine the problem considering the provided options.

Step 1: Recall the key relationships

• $AB \parallel CD$ implies that corresponding angles and alternate interior angles can be used.
• $\angle ACD = 150^\circ$.
• $\angle CAB = 90^\circ$.

Step 2: Re-calculate angle $x$

$x$ is the supplementary angle to $150^\circ$ because $\angle ACD$ is on a straight line. Thus: $x = 180^\circ - 150^\circ = 30^\circ$

Step 3: Re-calculate angle $y$

Using the triangle $\triangle ABC$: $\angle CAB + \angle ABC + \angle BCA = 180^\circ$ Given that $\angle CAB = 90^\circ$ and $x = 30^\circ$, then: $90^\circ + y + 30^\circ = 180^\circ$ $y = 180^\circ - 120^\circ = 60^\circ$

Conclusion:

• $x = 30^\circ$
• $y = 60^\circ$

Therefore, the correct option is B) 60, 30.

Would you like further details or have any other questions?

Related Questions:

1. Why is $\angle CAB$ considered as 90° in this scenario?
2. How would you solve the problem if the angle $\angle ACD$ were not given?
3. Can the angle $y$ ever be larger than $90^\circ$ in this figure?
4. What is the significance of the parallel lines in determining the angles?
5. How do corresponding angles help in solving geometry problems involving parallel lines?

Tip:

When working with triangles and parallel lines, always ensure to double-check the relationships between angles, particularly when supplementary or complementary angles are involved.