Two angles are supplementary if the sum of their measures equals 180 degrees.
Given:
- \( m<QRS = x + 16 \)
- \( m<SRT = 3x \)
Since they are supplementary, we can set up the equation:
\[ m<QRS + m<SRT = 180 \]
Substituting the expressions for the angles:
\[ (x + 16) + (3x) = 180 \]
Combining like terms:
\[ 4x + 16 = 180 \]
Now, subtract 16 from both sides:
\[ 4x = 180 - 16 \] \[ 4x = 164 \]
Next, divide by 4:
\[ x = \frac{164}{4} = 41 \]
Now that we have the value of \( x \), we can find \( m<SRT \):
\[ m<SRT = 3x = 3(41) = 123 \]
Therefore, the measure of \( <SRT \) is:
\[ \boxed{123} \]