https://file.aiquickdraw.com/mathbot/file/1727187259684vl8l116s.jpg

In the given diagram, the two angles are vertical angles, meaning they are equal to each other. We can set up the equation:

\[
2x - 13 = x + 17
\]

### Solving for \( x \):
1. Subtract \( x \) from both sides:
   \[
   2x - x - 13 = 17
   \]
   Simplifying, we get:
   \[
   x - 13 = 17
   \]

2. Add 13 to both sides:
   \[
   x = 17 + 13
   \]
   So,
   \[
   x = 30
   \]

The correct value of \( x \) is **30**, not 13 as marked in the image.

Would you like more details or have any questions?

Here are some related questions for practice:
1. What are vertical angles, and why are they equal?
2. Can you create an equation from other angles in intersecting lines?
3. If the equation was \(3x - 10 = 2x + 5\), what would the solution for \(x\) be?
4. How would the diagram change if the angles were supplementary?
5. What are some real-life applications of vertical angles?

**Tip:** Always check for angle relationships like vertical, complementary, or supplementary to set up correct equations in geometry problems!

Find the value of x in the diagram where two vertical angles are given as 2x - 13 and x + 17.

Learn how to solve for x in a diagram involving vertical angles, using the equation 2x - 13 = x + 17. This problem explores the Vertical Angles Theorem and basic algebra, suitable for students in Grades 7-9.

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