Since angles B and C are adjacent to angle A and since the sum of the angles around a point is 360°, we can use the fact that angle A and angle C are complementary (they share a vertex and are adjacent).
Given that \( m∠C = 75° \), we can use the relationship between angles adjacent to each other since they form a straight line together with angle A:
\[ m∠A + m∠C = 180° \]
Substituting the value of \( m∠C \):
\[ m∠A + 75° = 180° \]
Now, subtract 75° from both sides:
\[ m∠A = 180° - 75° = 105° \]
Thus, the measure of angle A is
\[ \boxed{105°} \]