Final answer:
When two lines are parallel, corresponding angles and alternate interior angles are equal. Therefore, θ1, θ3, and θ5 would be equal, as would θ2, θ4, and θ6. The correct answer is option B: θ2 = θ4, θ3 = θ6, θ1 = θ5.
Step-by-step explanation:
The question deals with the relationships between angles when two lines are parallel.
Using the properties of parallel lines and the angles formed by a transversal, which in this case are the lines intersecting lines p and q, there are specific angle relationships that can be observed.
When two lines are parallel, the following pairs of angles are equal due to being corresponding angles: θ1 = θ3 and θ2 = θ4. Similarly, because alternate interior angles are equal when the lines are parallel, θ3 = θ5 and θ4 = θ6.
Therefore, the set of angles that will be equal would be θ1 = θ3 = θ5 and θ2 = θ4 = θ6.
Based on the given statements, option B most closely resembles these relationships: θ2 = θ4, θ3 = θ6, θ1 = θ5. So, this set of statements would be true if line p is parallel to line q.