https://file.aiquickdraw.com/mathbot/file/17253921319358uqenk3s.jpg

The problem involves solving for the variables \( x \) and \( y \) using the given angles. Here's how you can solve it step by step.

### Given:
- \( m \angle XET = 90^\circ \)
- \( m \angle SEP = 5x - 4y + 2 \)
- \( m \angle PET = 3x + 2y \)

### Step 1: Understand the Relationships
The diagram shows that \( \angle XET \) is a right angle, meaning it equals \( 90^\circ \). The angles \( \angle SEP \) and \( \angle PET \) are adjacent and combine to form \( \angle XET \).

Therefore, the sum of the measures of \( \angle SEP \) and \( \angle PET \) must equal \( \angle XET \):
\[
m \angle SEP + m \angle PET = m \angle XET
\]
Substitute the given expressions:
\[
(5x - 4y + 2) + (3x + 2y) = 90
\]

### Step 2: Simplify the Equation
Combine like terms:
\[
5x + 3x - 4y + 2y + 2 = 90
\]
\[
8x - 2y + 2 = 90
\]

### Step 3: Isolate the Equation
Subtract 2 from both sides:
\[
8x - 2y = 88
\]

### Step 4: Simplify Further
Divide the entire equation by 2 to simplify:
\[
4x - y = 44
\]

### Step 5: Solve for \( y \)
You can express \( y \) in terms of \( x \) or continue with additional information if available. Assuming this is the only equation, we don't have enough information to solve for both \( x \) and \( y \) uniquely without more details.

However, if there's more information or a secondary equation not visible in the image, we could use that to find specific values for \( x \) and \( y \).

### Conclusion:
- The simplified equation is \( 4x - y = 44 \).
- Without additional data or equations, \( x \) and \( y \) can't be determined uniquely.

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Would you like more details on how to handle such problems, or do you have any additional information that could provide more context for a solution?  

### Follow-up Questions:
1. What is the specific method to solve systems of equations like this one?
2. How can you determine if there are infinitely many solutions or none at all for such systems?
3. What other relationships could exist between angles in similar geometric configurations?
4. What are the general steps to simplify linear equations?
5. How can graphing help visualize the solution of a system of equations?

### Tip:
Always check if the information provided is sufficient to solve for all variables, especially in systems of equations.

Solve for x and y using the angles provided in the geometric diagram with angle measurements: m∠XET = 90°, m∠SEP = 5x - 4y + 2, and m∠PET = 3x + 2y.

This problem involves solving for variables x and y by analyzing angle relationships in a geometric diagram. Learn how to use algebraic expressions and the angle sum theorem to find the solution, suitable for students in Grades 9-10.

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