https://file.aiquickdraw.com/mathbot/file/17272235912892ithhnj3.jpg

The image shows two parallel lines cut by a transversal, forming angles at points A, B, and C. Specifically, the angles involved are:

- \(\angle ABC\) is labeled as \(4x^\circ\),
- \(\angle ACB\) is labeled as \((3x + 23)^\circ\).

Since these two angles are on opposite sides of the transversal and inside the parallel lines, they are **alternate interior angles**. For parallel lines, alternate interior angles are congruent, meaning they are equal.

Therefore, we can set up the equation:
\[
4x = 3x + 23
\]

### Solving for \(x\):
\[
4x - 3x = 23
\]
\[
x = 23
\]

### Finding the measure of \(\angle ABC\):
Since \(\angle ABC = 4x\), we substitute \(x = 23\):
\[
\angle ABC = 4(23) = 92^\circ
\]

Thus, the measure of \(\angle ABC\) is \(92^\circ\).

Would you like more details or have any further questions?

Here are five related questions to think about:
1. What is the measure of \(\angle ACB\)?
2. How do alternate interior angles help in solving geometry problems?
3. Can you explain the relationship between corresponding angles when parallel lines are involved?
4. What are supplementary angles and how do they apply to transversal intersections?
5. What would happen if the lines were not parallel—how would that affect the angle relationships?

**Tip:** Always look for congruent or supplementary angles when parallel lines are involved to simplify calculations.

What is the measure of angle ABC in a transversal intersecting two parallel lines, where angle ABC is labeled as 4x degrees and angle ACB is labeled as (3x + 23) degrees?

Learn how to solve for angle ABC when two parallel lines are intersected by a transversal. The problem involves using the alternate interior angle theorem and algebraic manipulation. A step-by-step solution helps students in Grades 8-10 understand the relationship between the angles.

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