Angle \( P \) is the complementary angle of an angle measuring \( 65^{\circ} \). Angles \( P \) and \( Q \) are vertical angles. What is the measure of angle \( Q \) ?

To find the measure of angle \( Q \), we first need to determine the measure of angle \( P \). Since angle \( P \) is the complementary angle of the angle measuring \( 65^\circ \), we can use the fact that complementary angles add up to \( 90^\circ \). Therefore, we have: \[ P = 90^\circ - 65^\circ = 25^\circ \] Now, since angles \( P \) and \( Q \) are vertical angles and vertical angles are equal, we find that: \[ Q = P = 25^\circ \] Thus, the measure of angle \( Q \) is \( 25^\circ \).