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The image presents a problem involving parallel lines and transversals. We are asked to determine the measure of \(\angle 5\) if lines \(m \parallel n\) and \(\angle 2\) measures 35°.

### Step-by-Step Solution:

1. **Given:**
   - Lines \(m\) and \(n\) are parallel.
   - \(\angle 2 = 35^\circ\).
   - We are tasked with finding the measure of \(\angle 5\).

2. **Understanding Angle Relationships:**
   Since lines \(m\) and \(n\) are parallel, the angles formed by the transversal are related through the following types of angles:
   - Corresponding angles.
   - Alternate interior angles.
   - Same-side interior (or consecutive) angles.

3. **Step 1: Relationship Between \(\angle 2\) and \(\angle 6\):**
   \(\angle 2\) and \(\angle 6\) are **corresponding angles** because they are on the same side of the transversal and occupy the same relative position at each line. Since \(m \parallel n\), corresponding angles are congruent.
   
   Therefore, \[
   \angle 6 = \angle 2 = 35^\circ
   \]

4. **Step 2: Relationship Between \(\angle 5\) and \(\angle 6\):**
   \(\angle 5\) and \(\angle 6\) are **alternate interior angles**, which means they are equal as well when the lines are parallel.

   Therefore, \[
   \angle 5 = \angle 6 = 35^\circ
   \]

Thus, the measure of \(\angle 5\) is \(35^\circ\), not \(55^\circ\). Therefore, the correct answer seems to be \(35^\circ\), though it is not listed in the options.

Would you like more details or further clarification?

### Related Questions:
1. How do corresponding angles behave when two lines are parallel?
2. What is the difference between alternate interior angles and corresponding angles?
3. How do you find the measure of an angle formed by a transversal?
4. What are same-side interior angles, and how are they used in solving problems with parallel lines?
5. Why are parallel lines important in determining angle congruence?

### Tip:
When working with transversals and parallel lines, always look for angle pairs like corresponding, alternate interior, and same-side interior angles to establish relationships.

If line m is parallel to line n and angle 2 measures 35°, what is the measure of angle 5?

Learn how to calculate the measure of angle 5 when two lines are parallel and a transversal forms angle 2 measuring 35°. Using the corresponding and alternate interior angles theorems, this problem is suitable for students in Grades 7-9.

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