Two angles are supplementary if their measures add up to \(180^\circ\). Therefore, we can set up the following equation based on the measures provided:
\[ m∠QRS + m∠SRT = 180^\circ \]
Substituting the expressions for the angles, we get:
\[ (x + 16) + (3x) = 180 \]
Combining like terms, we have:
\[ 4x + 16 = 180 \]
Next, we will isolate \(4x\) by subtracting \(16\) from both sides:
\[ 4x = 180 - 16 \] \[ 4x = 164 \]
Now, we divide both sides by \(4\) to solve for \(x\):
\[ x = \frac{164}{4} = 41 \]
Now that we have the value of \(x\), we can find the measure of \(∠SRT\):
\[ m∠SRT = 3x = 3(41) = 123^\circ \]
Therefore, the measure of \(∠SRT\) is:
\[ \boxed{123^\circ} \]