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The problem states that you are given the measures of two angles, \( m \angle 2 = 7x - 20 \) and \( m \angle 6 = 4x + 13 \), and you need to solve for \( x \).

Since these angles seem to be in the context of parallel lines and a transversal, they could be either corresponding angles, alternate interior angles, or some other relationship. Given that the equation is asking for \( x \), I will assume these angles are either corresponding or alternate interior angles, meaning they are equal.

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

\[
7x - 20 = 4x + 13
\]

Now, solve for \( x \):

1. Subtract \( 4x \) from both sides:
\[
7x - 4x - 20 = 13
\]
\[
3x - 20 = 13
\]

2. Add 20 to both sides:
\[
3x = 33
\]

3. Divide by 3:
\[
x = 11
\]

So, the value of \( x \) is \( 11 \).

Would you like further clarification on any step?

Here are 5 questions related to this problem:
1. What is the relationship between alternate interior angles and corresponding angles?
2. How do you determine if angles are equal in parallel lines cut by a transversal?
3. Can angles be supplementary instead of equal in some cases? When?
4. What happens to the angle measures when \( x \) is substituted back into the equations?
5. Are there other methods to verify the solution for \( x \)?

**Tip:** Always check the relationships between angles (such as corresponding or alternate interior) when working with parallel lines cut by a transversal!

Given the measures of two angles, m∠2 = 7x - 20 and m∠6 = 4x + 13, solve for x.

Learn how to solve for x in a geometry problem involving angle measures m∠2 = 7x - 20 and m∠6 = 4x + 13. This problem focuses on parallel lines cut by a transversal and using algebra to find the unknown variable.

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