https://file.aiquickdraw.com/mathbot/file/17296348521084x34r5zf.jpg

In the diagram, you have three angles around point \( S \), which together form a straight line. Since the angles on a straight line add up to \( 180^\circ \), we can set up an equation using the given angles.

### The angles are:
- \( \angle QSP = 71^\circ \)
- \( \angle RSP = (9x - 6)^\circ \)
- \( \angle RSQ = (2x)^\circ \)

### Equation for a straight line:
\[
71^\circ + (9x - 6)^\circ + 2x^\circ = 180^\circ
\]

### Simplify the equation:
\[
71 + 9x - 6 + 2x = 180
\]
\[
65 + 11x = 180
\]

### Solve for \( x \):
\[
11x = 180 - 65
\]
\[
11x = 115
\]
\[
x = \frac{115}{11}
\]
\[
x \approx 10.45
\]

Thus, \( x \approx 10.45 \).

Would you like further clarification or a more detailed explanation?

Here are 5 related questions:
1. How do you derive the equation for angles on a straight line?
2. What happens if one angle is missing? Can we still solve for \( x \)?
3. How do supplementary angles relate to this problem?
4. How do you handle the algebra if \( x \) had been part of multiple terms?
5. What is the importance of rounding in this type of problem?

**Tip**: Always check your calculations by adding the angles to ensure they sum to \( 180^\circ \).

Which equation can be used to solve for x, given the angles around point S?

Learn how to solve for x by using the angles around a point in a geometry diagram. This problem covers the sum of angles on a straight line and solving linear equations. Suitable for students in Grades 8-10.

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