When two lines intersect, they create four angles that are related in the following ways:
- Adjacent angles (those that share a common side) are supplementary, meaning they add up to \(180^\circ\).
- Opposite angles (those that are across from each other) are equal.
Given that \( m\angle C = 75^\circ \), we can find \( m\angle A \):
Since angles \( A \) and \( C \) are opposite angles, we know that: \[ m\angle A = m\angle C = 75^\circ \]
However, angle \( B \) is adjacent to angles \( A \) and \( C \). Therefore, we need to determine \( m\angle B \): \[ m\angle B + m\angle C = 180^\circ \] \[ m\angle B + 75^\circ = 180^\circ \] \[ m\angle B = 180^\circ - 75^\circ = 105^\circ \]
Now, since angle \( D \) is opposite angle \( B \): \[ m\angle D = m\angle B = 105^\circ \]
Thus, we conclude:
- \( m\angle A = 75^\circ \)
- \( m\angle B = 105^\circ \)
- \( m\angle C = 75^\circ \)
- \( m\angle D = 105^\circ \)
So the value of \( m\angle A \) is: \[ \boxed{75} \]