Two angles are supplementary if their measures add up to \(180^\circ\). Given the measures of the angles:
\[ m∠QRS = (x + 16)^\circ \]
\[ m∠SRT = (3x)^\circ \]
We can set up the equation for supplementary angles:
\[ (x + 16) + (3x) = 180 \]
Combining like terms:
\[ x + 16 + 3x = 180 \]
\[ 4x + 16 = 180 \]
Now, subtract 16 from both sides:
\[ 4x = 180 - 16 \]
\[ 4x = 164 \]
Next, divide both sides by 4:
\[ x = \frac{164}{4} \]
\[ x = 41 \]
Now we can find the measure of \(m∠SRT\):
\[ m∠SRT = 3x = 3(41) = 123^\circ \]
Therefore, the measure of \(∠SRT\) is
\[ \boxed{123^\circ} \]