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)

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.