https://file.aiquickdraw.com/mathbot/file/172539145672258ymc5eu.jpg

The image contains a problem where you need to solve for \( x \) and \( y \). The problem involves angles and their relationships, likely using the fact that the sum of angles in certain configurations equals a known value.

### The given equations and information are:
1. \( m \angle XST = 90^\circ \)
2. \( m \angle SRT = 5x + 4y - 2 \)
3. \( m \angle PST = 7x + 2y - 1 \)

Additionally, it looks like the angles \( \angle XSR \), \( \angle RST \), and \( \angle PST \) are positioned such that their sum is \( 90^\circ \) as per the drawing and the given information.

### To solve for \( x \) and \( y \):
You can set up the equation by summing the angles that form \( m \angle XST \):

\[
m \angle XST = m \angle SRT + m \angle PST = 90^\circ
\]

This gives you:
\[
5x + 4y - 2 + 7x + 2y - 1 = 90
\]

### Simplifying the equation:
\[
(5x + 7x) + (4y + 2y) - 2 - 1 = 90
\]
\[
12x + 6y - 3 = 90
\]
\[
12x + 6y = 93
\]

Finally, simplify by dividing the entire equation by 3:
\[
4x + 2y = 31
\]

So, the simplified equation to solve is:
\[
4x + 2y = 31
\]

### Step to Solve:
- We have one equation, but since we need both \( x \) and \( y \), we'll need more information or additional equations to solve this system.

Do you have another equation or additional information from the diagram or problem statement?

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Would you like more details on solving this equation? Or any questions on this method?

Here are some related questions:
1. How can you solve for two variables when you have only one equation?
2. What do supplementary and complementary angles mean in geometry?
3. How do you determine if angles are congruent?
4. What is the significance of linear pairs of angles?
5. How can you verify if your solution to a system of equations is correct?

**Tip:** When dealing with angles in geometry, always consider if they are part of a known angle sum, such as a triangle (180°) or a right angle (90°).

Solve for x and y given the angles in the diagram: m∠XST = 90°, m∠SRT = 5x + 4y - 2, and m∠PST = 7x + 2y - 1.

Learn how to solve for x and y using the angle relationships given in a geometric diagram. This problem involves key concepts from geometry and algebra, making it suitable for students in Grades 8-10.

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