Two angles are complementary if their measures add up to 90 degrees. Given that \( m∠X = 53.4° \), we can find \( m∠W \) using the following equation:
\[ m∠W + m∠X = 90° \]
Substituting the value of \( m∠X \):
\[ m∠W + 53.4° = 90° \]
Now, subtract \( 53.4° \) from both sides:
\[ m∠W = 90° - 53.4° \]
Calculating this gives:
\[ m∠W = 36.6° \]
Therefore, the degree measure of \( ∠W \) is \( \boxed{36.6°} \).