Let x be the measurement of the angle.
The complement of an angle is 90 degrees minus the measurement of the angle.
So, the complement of x is 90 - x.
The problem states that x is 10 degrees more than its complement.
So, we can write the equation x = 10 + (90 - x).
Combining like terms, we get 2x = 100.
Dividing both sides by 2, we get x = 50.
Therefore, the measurement of the angle is 50 degrees.