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The image shows a pair of intersecting lines, forming vertical angles. The two expressions \( 2x - 10^\circ \) and \( x + 40^\circ \) represent the measures of these vertical angles.

Since vertical angles are always equal, we can set the expressions equal to each other:

\[
2x - 10^\circ = x + 40^\circ
\]

Let's solve for \( x \):

1. Subtract \( x \) from both sides:
\[
2x - x - 10^\circ = 40^\circ
\]
\[
x - 10^\circ = 40^\circ
\]

2. Add \( 10^\circ \) to both sides:
\[
x = 50^\circ
\]

Thus, \( x = 50^\circ \).

Now, we can substitute \( x = 50^\circ \) back into the expressions for the angles to find their measures:

- \( 2x - 10^\circ = 2(50^\circ) - 10^\circ = 100^\circ - 10^\circ = 90^\circ \)
- \( x + 40^\circ = 50^\circ + 40^\circ = 90^\circ \)

So, both angles are \( 90^\circ \).

Let me know if you'd like more details or have further questions. Here are five related questions to explore:

1. What are vertical angles, and why are they always equal?
2. How do you solve for unknowns in linear equations like the one we solved here?
3. Can vertical angles ever be supplementary (sum to 180°)?
4. What are alternate interior angles, and how do they relate to this problem?
5. How would you solve for \( x \) if the two angles given were supplementary instead of equal?

**Tip:** Always check for the relationship between angles when working with intersecting lines; it helps determine the correct equation to solve!

Solve for x in the given vertical angle problem: 2x - 10° and x + 40° are vertical angles.

Learn how to solve a vertical angle problem where the measures of the angles are 2x - 10° and x + 40°. This solution involves basic geometry and algebra concepts, suitable for students in Grades 7-9.

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