In the scenario you described, when two lines intersect, the angles formed have some important relationships. Angles that are adjacent (next to one another) on a straight line are supplementary, meaning their measures add up to \(180^\circ\).
Since angle \(C\) is given as \(75^\circ\), we can find the measure of angle \(B\) next to it:
\[ m\angle B + m\angle C = 180^\circ \]
Substituting the value of \(m\angle C\):
\[ m\angle B + 75^\circ = 180^\circ \]
Now, solving for \(m\angle B\):
\[ m\angle B = 180^\circ - 75^\circ = 105^\circ \]
Now looking at angles \(A\) and \(B\), we see that they are also adjacent angles on a straight line:
\[ m\angle A + m\angle B = 180^\circ \]
Substituting the value of \(m\angle B\):
\[ m\angle A + 105^\circ = 180^\circ \]
Now, we solve for \(m\angle A\):
\[ m\angle A = 180^\circ - 105^\circ = 75^\circ \]
Therefore, the measure of angle \(A\) is:
\[ \boxed{75^\circ} \]