To solve this problem, let's analyze the angles formed by the parallel lines and the transversal:

1. We are given that $m \angle 3 = 102^\circ$.

2. Since angles 3 and 5 are corresponding angles (formed by the transversal crossing the parallel lines), they are equal. Therefore: $m \angle 5 = 102^\circ$

3. Similarly, angles 3 and 8 are alternate exterior angles. For two parallel lines cut by a transversal, alternate exterior angles are also equal. Thus: $m \angle 8 = 102^\circ$

Solution Summary:

• $m \angle 5 = 102^\circ$
• $m \angle 8 = 102^\circ$

Would you like further clarification on any of these steps?

Here are 5 related questions that expand on this information:

1. What are the properties of corresponding angles when two parallel lines are cut by a transversal?
2. How can you determine the measure of angle 1 in this diagram?
3. If $m \angle 4$ was given, how could you find $m \angle 7$?
4. What are alternate interior angles, and which angles in this diagram are alternate interior angles?
5. How would the solution change if the lines were not parallel?

Tip: Remember that corresponding and alternate angles are only equal when the lines involved are parallel.