To solve for the angles $x$ and $y$ in this diagram, let's break it down step by step.

Problem 17: Finding the value of angle $x$

In the diagram, we are given:

• One angle is 50°.
• There is a right triangle, and angle $x$ is part of this triangle. Notice that there is a right angle marked next to $x$, meaning the sum of the angles in this smaller triangle must be 180° (since it is a triangle).

For the smaller triangle:

• One angle is given as 50°.
• The right angle is 90°.

Using the triangle sum theorem (which states that the sum of angles in a triangle is always 180°), we can find angle $x$ as follows: $x = 180° - 90° - 50° = 40°$

So, the value of $x$ is 40°, but this option isn't listed among the answers, which suggests a possible error in the diagram or options. However, this is the correct calculation based on the given angles.

Problem 18: Finding the value of angle $y$

To find angle $y$, notice that it is part of a straight line. A straight line always adds up to 180°.

From the given information:

• The angle adjacent to $y$ is the sum of angles $50° + x$. So, this adjacent angle is: $50° + 40° = 90°$

Now, using the fact that the angles on a straight line add up to 180°: $y = 180° - 90° = 90°$

Again, this doesn't match the provided answer options for $y$, but this is the correct mathematical solution based on the diagram.

Conclusion:

• For $x$, the value should be 40°, but this isn't listed in the options.
• For $y$, the value should be 90°, which is also not listed in the options.

Let me know if you would like further clarification or to adjust for any possible missing details.

Would you like me to explain more or address any doubts?

Here are five related questions you might find helpful:

1. What is the sum of angles in a triangle?
2. How do adjacent angles on a straight line add up?
3. What is the meaning of a right angle?
4. How can you apply the triangle sum theorem in various problems?
5. What are some properties of supplementary angles?

Tip: In any triangle, the sum of all internal angles will always equal 180°, no matter what type of triangle it is.