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In the image, two parallel lines are cut by a transversal, and you are asked to find the measures of angles \( \angle 2 \) and \( \angle 4 \), given that the measure of \( \angle 5 = 139^\circ \).

Here’s how we can solve it using angle relationships for parallel lines and a transversal:

1. **Corresponding Angles**:
   - \( \angle 5 \) and \( \angle 1 \) are corresponding angles, so \( m \angle 1 = 139^\circ \).

2. **Alternate Interior Angles**:
   - \( \angle 1 \) and \( \angle 2 \) are alternate interior angles, which means they are congruent. So, \( m \angle 2 = 139^\circ \).

3. **Linear Pair**:
   - \( \angle 4 \) and \( \angle 5 \) form a linear pair. Linear pairs are supplementary, meaning the sum of their measures is \( 180^\circ \). Therefore, \( m \angle 4 = 180^\circ - 139^\circ = 41^\circ \).

### Final Answer:
- \( m \angle 2 = 139^\circ \)
- \( m \angle 4 = 41^\circ \)

Let me know if you need further clarification or details.

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Here are 5 related questions to deepen understanding:

1. How would you identify alternate exterior angles in the same diagram?
2. If \( m \angle 6 \) was given, how could you find \( m \angle 3 \)?
3. What is the relationship between corresponding angles in parallel lines cut by a transversal?
4. Can you explain how vertical angles relate in this diagram?
5. If \( m \angle 3 = 80^\circ \), what would be the measure of \( m \angle 7 \)?

**Tip**: Remember that corresponding and alternate interior angles are congruent when parallel lines are cut by a transversal. This simplifies finding unknown angles.

Two parallel lines are cut by a transversal. Given that m∠5 = 139°, find m∠2 and m∠4.

Solve the problem of finding the measures of angles 2 and 4 when two parallel lines are cut by a transversal, and m∠5 = 139°. This involves the use of the Alternate Interior Angles Theorem and the Linear Pair Theorem, suitable for students in Grades 7-9.

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