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The image you provided contains two problems involving angles in a geometric diagram. Let's analyze and solve each of them:

### Problem 15: What is the value of angle \( x \)?
From the diagram, we see a right triangle \( \triangle ABD \) with angle \( x \) at \( A \), and angle \( \angle DAB = 90^\circ \). There is also a 330° angle at \( C \), though it doesn't seem to be directly relevant for solving for \( x \). The triangle looks to be isosceles, as the two legs (other than the hypotenuse) seem to have equal length, implying that the two base angles are equal.

- In an isosceles right triangle, the angles would be \( 45^\circ \), which corresponds to option \( B: 45^\circ \).

Thus, the value of \( x = 45^\circ \).

### Problem 16: What is the value of angle \( y \)?
In the same triangle, the angle \( y \) appears to be the angle at vertex \( B \) of the triangle.

Since we determined that \( \triangle ABD \) is isosceles with angle \( \angle ADB = 45^\circ \), the remaining angle, \( \angle ABD \), would also be \( 45^\circ \).

Thus, the value of \( y = 45^\circ \), which corresponds to option \( B: 45^\circ \).

### Answers:
- Problem 15: \( x = 45^\circ \) (Option B)
- Problem 16: \( y = 45^\circ \) (Option B)

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Would you like further clarification on any part of this solution, or details on why it's an isosceles right triangle? 

Here are 5 questions that expand on this topic:
1. How do you recognize an isosceles right triangle from its diagram?
2. Why do the angles in a right triangle sum to 180°?
3. What are the general properties of an isosceles triangle?
4. How would you calculate angles in non-right triangles?
5. What role does the 330° angle play in the problem, if any?

**Tip:** Always check the triangle's properties first—whether it's isosceles, equilateral, or scalene—as this will often simplify angle calculations.

What are the values of angles x and y in the given triangle?

Find the values of angles x and y in a right isosceles triangle. This problem involves key concepts such as the Isosceles Triangle Theorem and properties of right triangles. Suitable for students in Grades 7-9.

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