Final answer:
Moving point B along line BC changes the measure of angle ABC; the angle increases as point B moves closer to C and decreases as it moves away from C. However, other angles like MBA and ma remain constant because they do not involve line BC. Moving point C changes the length of BC but does not affect the measure of angle ABC.
Step-by-step explanation:
When you move point B along line BC, the measure of angle ABC (m∠ABC) changes. Specifically, if point B moves closer to point C, m∠ABC becomes larger, and if point B moves away from point C towards point A, the angle decreases. The measure of MBA and ma (m∠MBA and m∠A, assuming these are two different angles) would not change by moving point B along line BC, as those angles are not defined with respect to line BC or do not contain line BC within them.
However, when you move point C away from point B along line BC, the size of angle ABC does not change because it is still the angle between line AB and line BC; what changes is the length of side BC. But the measure of MBA and ma would still remain the same for the same reasons described above; these angles do not involve line BC directly. It's important to remember that in geometry, the length of sides can change without necessarily affecting the measures of angles that are not connected to those sides.