Since triangles \( \triangle XYZ \) and \( \triangle RST \) are similar (denoted by \( \triangle XYZ \sim \triangle RST \)), the corresponding angles are equal.
Given:
- \( m\angle X = 50^\circ \)
- \( m\angle S = 79^\circ \)
To find \( m\angle T \), we first need to determine \( m\angle Y \). The sum of the angles of triangle \( XYZ \) is \( 180^\circ \):
\[ m\angle X + m\angle Y + m\angle Z = 180^\circ \] \[ 50^\circ + m\angle Y + m\angle Z = 180^\circ \] \[ m\angle Y + m\angle Z = 130^\circ \tag{1} \]
Similarly, for triangle \( RST \), the sum of the angles is also \( 180^\circ \):
\[ m\angle R + m\angle S + m\angle T = 180^\circ \] Since \( \triangle XYZ \sim \triangle RST \), \[ m\angle Y = m\angle R \quad \text{and} \quad m\angle Z = m\angle T \] Therefore, we can express \( m\angle T \) as follows:
From angle \( S \): \[ m\angle R + 79^\circ + m\angle T = 180^\circ \tag{2} \]
Now, we know \( m\angle R = m\angle Y \). Substituting \( m\angle Y \) from equation (1):
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Start with equation (1): \[ m\angle R + m\angle Z = 130^\circ \]
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Substituting \( m\angle R = m\angle Y \) and solving for \( m\angle Z \): \[ m\angle Z = 130^\circ - m\angle R \]
Substituting into equation (2) gives us:
\[ (130^\circ - m\angle Z) + 79^\circ + m\angle T = 180^\circ \] Here, \( m\angle Z = m\angle T \). Thus, \[ (130^\circ - m\angle T) + 79^\circ + m\angle T = 180^\circ \] \[ 130^\circ + 79^\circ = 180^\circ \] \[ 209^\circ - m\angle T = 180^\circ \] Subtracting \( 209^\circ \) from both sides gives: \[ m\angle T = 29^\circ \]
Thus, the measure of angle \( T \) is:
\[ \boxed{29^\circ} \]