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To solve for the values of \( x \) and \( y \), we need to utilize the fact that the sum of all angles around point \( V \) must add up to 360°. In the diagram, we have the following angles at point \( V \):

1. \( \angle PVQ = 36^\circ \)
2. \( \angle QVR = 5x \)
3. \( \angle RVS = 4x \)
4. \( \angle SVT = 3y \)
5. The remaining angle \( \angle TVU \) is a right angle, so it is \( 90^\circ \).

### Step-by-Step Process:

1. Sum of angles around a point: 
   \[
   36^\circ + 5x + 4x + 3y + 90^\circ = 360^\circ
   \]

2. Simplify the equation:
   \[
   126^\circ + 9x + 3y = 360^\circ
   \]

3. Subtract 126° from both sides:
   \[
   9x + 3y = 234^\circ
   \]

4. Divide the entire equation by 3 to simplify:
   \[
   3x + y = 78^\circ
   \]

Now we have the equation \( 3x + y = 78 \). We need additional information or a system of equations to solve for both \( x \) and \( y \), but based on the current information, this is the relationship between \( x \) and \( y \).

### Next Steps:
You could now use any further conditions, or test specific values of \( x \) to find corresponding \( y \), but if there's no other information provided, this is the final form.

Would you like further details or to ask any questions about this solution?

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Here are some related questions for further exploration:
1. How can we use substitution or trial methods to find possible values of \( x \) and \( y \)?
2. How do we approach solving angles in similar geometric problems?
3. What methods can help check consistency in geometry problems?
4. Can different angle systems yield different results? 
5. How do right angles influence the distribution of surrounding angles?

**Tip:** Always use the rule that angles around a point sum to 360° for problems like these!

Solve the problem of finding x and y by using the angle sum property where the sum of angles around a point is 360°. This detailed solution involves setting up an equation and simplifying it. Suitable for students in Grades 8-10.

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