Given that triangle XYZ is similar to triangle RST (denoted as \( \triangle XYZ \sim \triangle RST \)), we can use the properties of similar triangles.
Since the sum of the angles in a triangle is always 180 degrees, we can find the measurement of angle T using angle S and the other angle in triangle RST.
First, we find the measure of angle R:
\[ \text{Measure of angle R} = 180^\circ - \text{Measure of angle S} - \text{Measure of angle T} \]
However, we don't have the measure of angle T yet, but we can find it.
We know angle X is 50 degrees and angle S is 79 degrees. Now, since corresponding angles are equal in similar triangles, angle X corresponds with angle R, and angle S corresponds with angle T.
Using the triangle sum property for triangle RST:
\[ \text{Measure of angle R} = 180^\circ - \text{Measure of angle S} - \text{Measure of angle T} \]
From the similarity, we know:
\[ \text{Measure of angle X} + \text{Measure of angle Y} + \text{Measure of angle Z} = 180^\circ \] also corresponds to: \[ \text{Measure of angle R} + \text{Measure of angle S} + \text{Measure of angle T} = 180^\circ \]
Since we don't have the Measure of angle Y or angle Z, we can't explicitly find angle T directly from the provided data. However, we can use that angle R matches with angle X.
If angle S is 79 degrees (and corresponds to angle T), we can find angle T:
\[ \text{Measure of angle T} = 180^\circ - \text{Measure of angle R} - \text{Measure of angle S} \]
From this, we can set this up with values:
As we know Measure of angle R should be the same as Measure of angle X (which is 50 degrees):
Thus: \[ T = 180^\circ - 50^\circ - 79^\circ \]
Finally calculating: \[ T = 180 - 50 - 79 = 51^\circ \]
Therefore, the measure of angle T is 51 degrees.
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