Since triangle \(XYZ\) is similar to triangle \(RST\) (denoted as \(triangle XYZ \sim triangle RST\)), the corresponding angles of the triangles are equal.
Given:
- \(m\angle X = 40^\circ\)
- \(m\angle S = 75^\circ\)
To find \(m\angle T\):
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First, we can find \(m\angle R\): Since the angles in a triangle sum up to \(180^\circ\), \[ m\angle R = 180^\circ - m\angle S - m\angle T \]
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Now we know the following relationships from the similarity:
- \(m\angle X = m\angle R\)
- \(m\angle S = m\angle T\)
So we can say: \[ 40^\circ = m\angle R \quad (1) \] \[ 75^\circ = m\angle T \quad (2) \]
- To find \(m\angle T\): Using equation (2) directly, \[ m\angle T = 75^\circ \]
Thus, the measure of angle \(T\) is \(75^\circ\).
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