Since triangles \( \triangle XYZ \) and \( \triangle RST \) are similar (noted as \( \triangle XYZ \sim \triangle RST \)), their corresponding angles are equal.
We are given:
- \( m\angle X = 50^\circ \)
- \( m\angle S = 79^\circ \)
To find \( m\angle T \), we can use the property of similar triangles where the sum of the angles in a triangle equals \( 180^\circ \).
First, we can find \( m\angle R \): \[ m\angle R = 180^\circ - m\angle X - m\angle S \] Substituting the known values: \[ m\angle R = 180^\circ - 50^\circ - 79^\circ \] \[ m\angle R = 180^\circ - 129^\circ = 51^\circ \]
Since \( \triangle XYZ \sim \triangle RST \), we have that \( m\angle T = m\angle R \): \[ m\angle T = 51^\circ \]
Thus, the measure of angle \( T \) is \( \boxed{51^\circ} \).
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