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.