Two angles are supplementary if their measures add up to \(180^\circ\). In this case, we have:
\[ m∠QRS + m∠SRT = 180^\circ \]
Substituting the given measures:
\[ (x + 16) + (3x) = 180^\circ \]
Now, combine like terms:
\[ 4x + 16 = 180^\circ \]
Next, subtract \(16\) from both sides:
\[ 4x = 164^\circ \]
Now, divide by \(4\):
\[ x = 41^\circ \]
Now we can find the measure of \( ∠SRT \):
\[ m∠SRT = 3x = 3(41) = 123^\circ \]
Thus, the measure of \( ∠SRT \) is:
\[ \boxed{123^\circ} \]