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The diagram you provided shows two parallel lines, \( r \) and \( s \), cut by a transversal \( q \). We're given that \( m\angle 2 = 70^\circ \), and we are asked to find \( m\angle 5 \).

### Step-by-step solution:

1. **Identify relationships between angles:**
   - Since \( r \parallel s \), we can use properties of parallel lines and transversals.
   - Angles 2 and 6 are **corresponding angles**, which means they are congruent. Therefore:
     \[
     m\angle 6 = m\angle 2 = 70^\circ
     \]
   
2. **Identify the relationship between angles 6 and 5:**
   - Angles 5 and 6 are **linear pairs**, meaning their sum is \( 180^\circ \) because they are on a straight line. Therefore:
     \[
     m\angle 5 + m\angle 6 = 180^\circ
     \]
     Substituting \( m\angle 6 = 70^\circ \):
     \[
     m\angle 5 + 70^\circ = 180^\circ
     \]
     Solving for \( m\angle 5 \):
     \[
     m\angle 5 = 180^\circ - 70^\circ = 110^\circ
     \]

Thus, the measure of \( \angle 5 \) is \( 110^\circ \).

Let me know if you'd like more details or have any questions. Here are some related questions to expand on this concept:

1. What are the other corresponding angles in the diagram?
2. What is the measure of \( \angle 8 \)?
3. How would you find the measure of \( \angle 4 \)?
4. Can you identify any pairs of alternate interior angles?
5. What can you say about vertical angles in this diagram?

**Tip:** When working with parallel lines and transversals, look for corresponding, alternate interior, and vertical angles to find unknown angle measures quickly.

Learn how to find the measure of angle 5 in a diagram involving parallel lines cut by a transversal. With m∠2 = 70°, use corresponding angles and linear pair properties to determine m∠5. Suitable for students in Grades 7-10.

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