Two angles are considered complementary if the sum of their measures is 90 degrees.
Given one angle is 66 degrees, you can find the measure of angle X (denoted as /_x) by using the formula:
\[ /_x = 90^\circ - 66^\circ \]
Calculating this gives:
\[ /_x = 24^\circ \]
Therefore, the measure of angle X is 24 degrees.