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The figure shows two intersecting lines, with angles labeled \( 58^\circ \) and \( 2x^\circ \) as adjacent angles. These angles are **alternate interior angles** because they are on opposite sides of the transversal and inside the parallel lines.

Since alternate interior angles are congruent, we can set up the following equation:
\[
2x = 58
\]

Now, solve for \( x \):

\[
x = \frac{58}{2} = 29
\]

Thus, the value of \( x \) is \( 29 \).

Would you like more details on alternate interior angles or any other part of this explanation?

Here are 5 related questions to expand this concept:

1. What is the relationship between corresponding angles and alternate interior angles?
2. How would the equation change if the angles were supplementary instead of congruent?
3. How do you determine which angles are alternate interior angles in a more complex figure?
4. What is the general rule for angles formed by two parallel lines and a transversal?
5. Can the transversal be at any angle, or does it have to be perpendicular to the parallel lines?

**Tip**: When working with parallel lines and a transversal, always remember that alternate interior angles are equal if the lines are parallel.

Find the value of x using the figure, shown to the right. The figure shows two intersecting lines with angles labeled 58° and 2x°. The value of x is __ (Simplify your answer. Do not include the degree symbol in your answer).

Learn how to solve for x when given a pair of alternate interior angles, one of which is 58° and the other 2x°. This problem uses the Alternate Interior Angles Theorem and requires solving a linear equation. Suitable for students in Grades 7-9.

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