Since the 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 can use the fact that the sum of angles in a triangle is \(180^\circ\).
First, calculate \(m\angle Y\): \[ m\angle Y = 180^\circ - m\angle X - m\angle Z \]
But since we don't have \(m\angle Z\), we will calculate \(m\angle R\) next. The angles in \(\triangle RST\) also sum up to 180°:
Let \(m\angle R = m\angle X\) (since corresponding angles in similar triangles are equal) and \(m\angle T = m\angle Z\). So, we can express \(m\angle R\) and \(m\angle T\) in terms of angles in triangle RST.
To find \(m\angle R\): \[ m\angle R = m\angle X = 50^\circ \]
Now, find \(m\angle T\): Using the angle sum property of triangle RST, \[ m\angle R + m\angle S + m\angle T = 180^\circ \] Substituting the known angles: \[ 50^\circ + 79^\circ + m\angle T = 180^\circ \] \[ 129^\circ + m\angle T = 180^\circ \] Now, isolate \(m\angle T\): \[ m\angle T = 180^\circ - 129^\circ = 51^\circ \]
Thus, the measure of angle \(T\) is: \[ \boxed{51^\circ} \]