Final answer:
When lines m and n are parallel, angles 1 and 6 are corresponding angles and are, therefore, equal in measure.
Step-by-step explanation:
If m and n are parallel lines, then the relationship between angles 1 and 6 would be that they are corresponding angles. When lines m and n are parallel, angles 1 and 6 are corresponding angles and are, therefore, equal in measure. Corresponding angles are equal in measure when two lines are parallel and a transversal crosses them.
In this case, since lines m and n are parallel, angle 1 and angle 6 are on the same side of the transversal and are in corresponding positions relative to the parallel lines. Hence, the measure of angle 1 is equal to the measure of angle 6.
This is a fundamental concept in geometry related to parallel lines and transversals, and it is often used to solve problems involving angle measurements and proofs.