Angle e and angle f are complementary. The measure of angle e is 54 degrees more than the measure of angle f. Find the measure of each angle.

1. Given that \( e \) and \( f \) are complementary, we know
e + f = 90^\circ

2. We are told that \( e \) is 54 degrees more than \( f \), so
e = f + 54^\circ

3. Substitute the second equation into the first equation:
(f + 54^\circ) + f = 90^\circ

4. Combine like terms:
2f + 54^\circ = 90^\circ

5. Subtract 54 degrees from both sides:
2f = 36^\circ

6. Divide by 2:
f = 18^\circ

7. Now, substitute \( f = 18^\circ \) back into the equation \( e = f + 54^\circ \):
e = 18^\circ + 54^\circ
e = 72^\circ

Therefore, the measures of the angles are:
e = 72^\circ, \, f = 18^\circ