Let's denote the measure of the angle as x degrees.
The complementary angle is 90 - x degrees, since the sum of an angle and its complementary angle is always 90 degrees.
According to the given information, the angle measures 30.8 degrees more than its complementary angle, so we can set up the equation:
x = (90 - x) + 30.8
Now, let's solve for x:
x = 90 - x + 30.8
2x = 90 + 30.8
2x = 120.8
x = 120.8/2
x = 60.4
Therefore, the measure of the angle is 60.4 degrees, and its complementary angle is 90 - 60.4 = 29.6 degrees.