This problem involves two parallel lines $a$ and $b$ intersected by a transversal line, creating several angles. We are given that $m\angle 2 = 122^\circ$, and the task is to determine $m\angle 3$.

Here's how to solve this:

1. Identify the relationship between angles 2 and 3: Since lines $a$ and $b$ are parallel, angle 2 and angle 3 are alternate interior angles formed by the transversal intersecting the parallel lines. Alternate interior angles are always congruent.

2. Therefore, $m\angle 3 = m\angle 2 = 122^\circ$.

Thus, the measure of $\angle 3$ is 122°.

Would you like further details or clarifications?

5 Related Questions:

1. What is the sum of the interior angles on one side of a transversal?
2. What are alternate exterior angles, and how are they related to parallel lines?
3. How can you identify corresponding angles in parallel line diagrams?
4. Can you always use the property of vertical angles when lines are parallel?
5. How can angle relationships help in solving real-world design problems?

Tip:

When working with parallel lines and a transversal, remember the relationships between alternate interior, alternate exterior, and corresponding angles. These are key to quickly solving angle-based problems!