https://file.aiquickdraw.com/mathbot/file/1727460152714dwyq27f4.jpg

The image shows two intersecting lines, with angles formed by expressions \(17x - 1\) and \(15x + 5\). Since the angles are opposite each other, they are called **vertically opposite angles**, and vertically opposite angles are always equal.

We can set the expressions equal to each other and solve for \(x\):

\[
17x - 1 = 15x + 5
\]

Let's solve this equation step-by-step.

1. Subtract \(15x\) from both sides:
\[
17x - 15x - 1 = 5
\]
\[
2x - 1 = 5
\]

2. Add 1 to both sides:
\[
2x = 6
\]

3. Divide both sides by 2:
\[
x = 3
\]

Thus, \(x = 3\).

Would you like more details on this solution or have any further questions?

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Here are 5 questions related to the above solution for practice:
1. What are vertically opposite angles, and why are they always equal?
2. How do you verify that two angles are equal in an equation?
3. What would happen if the angles were supplementary instead of equal?
4. What is the value of the angle if you substitute \(x = 3\) back into the expressions?
5. Can this method be used to solve for angles in any other geometric configurations?

**Tip:** When solving linear equations, always isolate the variable by performing inverse operations step-by-step.

Two intersecting lines form vertically opposite angles, represented by the expressions 17x - 1 and 15x + 5. Solve for x.

Learn how to solve for x in a vertically opposite angle problem, where the angles are represented by 17x - 1 and 15x + 5. This detailed step-by-step solution uses algebra and the theorem of vertically opposite angles, suitable for students in Grades 7-9.

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