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To solve the problem, we need to determine the measure of angle \( \angle 2 \) based on the given information. 

The image shows two parallel lines cut by a transversal, with angles labeled using algebraic expressions. Let's analyze:

- The angles \( (7x + 1)^\circ \) and \( (18x + 4)^\circ \) are provided in the diagram.
- Since the two lines are parallel, and these angles are corresponding angles (on the same side of the transversal and at corresponding positions), they must be equal.

Thus, we set up the equation:

\[
7x + 1 = 18x + 4
\]

### Solving for \( x \):
\[
7x - 18x = 4 - 1
\]
\[
-11x = 3
\]
\[
x = -\frac{3}{11}
\]

Now, we substitute \( x = -\frac{3}{11} \) back into either expression to find the value of \( \angle 1 \). Using \( 7x + 1 \):

\[
7\left(-\frac{3}{11}\right) + 1 = -\frac{21}{11} + 1 = -\frac{21}{11} + \frac{11}{11} = -\frac{10}{11}^\circ
\]

Since this result is quite small and negative, it seems something might be off in either assumption or calculation.

I'll review and clarify

Learn how to solve for the measure of angle ∠2 in a geometry problem involving parallel lines and transversals. This problem uses algebraic equations and the Corresponding Angles Theorem, making it ideal for students in Grades 8-10.

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