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.