Since triangle XYZ is similar to triangle RST (denoted as triangleXYZ ~ triangleRST), the corresponding angles of the two triangles are congruent.
We know:
- m∠X = 50 degrees
- m∠S = 79 degrees
To find the measure of angle T, we can use the property that the sum of the angles in a triangle is always 180 degrees.
First, let's find the measure of angle Y in triangle XYZ. Since triangle XYZ ~ triangle RST, we have:
\[ m\angle Y + m\angle X + m\angle Z = 180^{\circ} \]
Since we don't know m∠Z yet, let’s analyze triangle RST to find the missing angle.
In triangle RST, we can use the same angle sum property:
\[ m\angle R + m\angle S + m\angle T = 180^{\circ} \]
We know m∠S (79 degrees), and we need to find m∠R, which corresponds to m∠X (50 degrees):
So that means:
- m∠R = m∠X = 50 degrees
Now we can find m∠T in triangle RST:
\[ 50 + 79 + m\angle T = 180^{\circ} \]
Adding the known angles:
\[ 129 + m\angle T = 180^{\circ} \]
Now, subtract 129 from both sides:
\[ m\angle T = 180^{\circ} - 129^{\circ} = 51^{\circ} \]
Thus, the measure of angle T is \( \boxed{51} \) degrees.