Since triangles \( \triangle XYZ \) and \( \triangle RST \) are similar (denoted as \( \triangle XYZ \sim \triangle RST \)), their corresponding angles are equal.
Given:
- \( m\angle X = 50^\circ \)
- \( m\angle S = 79^\circ \)
To find the measure of angle \( T \), we first calculate the measure of angle \( Y \) in triangle \( XYZ \).
The sum of the angles in a triangle is \( 180^\circ \). Therefore,
\[ m\angle Y = 180^\circ - m\angle X - m\angle Z \]
However, we need \( m\angle R \) in triangle \( RST \) which would correspond to angle \( Y \) in triangle \( XYZ \).
Since angle \( S \) corresponds to angle \( Y \) due to similarity, we have:
\[ m\angle Y = m\angle R = 79^\circ \]
Now we can calculate \( m\angle T \):
Using the triangle angle sum for triangle \( RST \):
\[ m\angle R + m\angle S + m\angle T = 180^\circ \]
Substituting the known values:
\[ 79^\circ + 50^\circ + m\angle T = 180^\circ \]
This simplifies to:
\[ m\angle T = 180^\circ - 79^\circ - 50^\circ \] \[ m\angle T = 180^\circ - 129^\circ \] \[ m\angle T = 51^\circ \]
Thus, the measure of angle \( T \) is
\[ \boxed{51^\circ} \]