1. The problem asks to find the values of angles $y$ and $z$ in triangle $UVT$ where the angle at vertex $T$ is $45^\circ$. 2. Recall that the sum of interior angles in any triangle is always $180^\circ$. This means: $$y + z + 45^\circ = 180^\circ$$ 3. To find $y$ and $z$, we need more information about the triangle, such as side lengths or other angle measures. Since the problem does not provide these, we can only express $y$ and $z$ in terms of each other: $$y + z = 180^\circ - 45^\circ = 135^\circ$$ 4. Without additional data, the exact values of $y$ and $z$ cannot be determined individually, only their sum is known. Final answer: $$y + z = 135^\circ$$