In the provided image, we have two parallel lines cut by a transversal, creating two marked angles: $(2x - 23)^\circ$ and $(x + 2)^\circ$. Since the lines are parallel, the marked angles are alternate interior angles, which means they are congruent (equal).

Thus, we can set up the following equation:

$2x - 23 = x + 2$

Solving for $x$:

1. Subtract $x$ from both sides:

$2x - x - 23 = 2$

$x - 23 = 2$

2. Add 23 to both sides:

$x = 25$

Finding the measure of each angle:

• Substitute $x = 25$ into $(2x - 23)^\circ$:

$2(25) - 23 = 50 - 23 = 27^\circ$

• Substitute $x = 25$ into $(x + 2)^\circ$:

$25 + 2 = 27^\circ$

Thus, both angles are $27^\circ$.

Would you like any additional details or further explanation?

Here are 5 related questions:

1. What are alternate interior angles?
2. How do you determine if two angles are congruent when parallel lines are involved?
3. Can alternate interior angles be supplementary? Why or why not?
4. How would the solution change if the lines were not parallel?
5. What other angle relationships are formed when two parallel lines are cut by a transversal?

Tip: Always check for congruent angle relationships like alternate interior, corresponding, or vertically opposite angles when working with parallel lines.