Two angles are complementary if the sum of their measures equals 90 degrees.
Given that one angle measures 27°, we can find the measure of angle \( x \) by using the formula:
\[ x + 27° = 90° \]
To solve for \( x \), subtract 27° from both sides:
\[ x = 90° - 27° \] \[ x = 63° \]
Therefore, the measure of angle \( x \) is:
\[ x = 63° \]