We are given a diagram with two parallel lines, $TW$ and $UV$, and a transversal intersecting them. We are given that $\angle T = 104^\circ$ and $\angle V = 57^\circ$. We need to find the measure of $\angle TUV$ and $\angle VWT$.

1. Problem Description

We are given a diagram with two parallel lines, $TW$ and $UV$, and a transversal intersecting them. We are given that $\angle T = 104^\circ$ and $\angle V = 57^\circ$. We need to find the measure of $\angle TUV$ and $\angle VWT$.

2. Solution Steps

a) Find $\angle TUV$.

Since $TW \parallel UV$, the interior angles on the same side of the transversal are supplementary. Therefore, $\angle T + \angle U = 180^\circ$.

$$$$

\angle T + \angle U = 180^\circ \\

104^\circ + \angle TUV = 180^\circ \\

\angle TUV = 180^\circ - 104^\circ \\

\angle TUV = 76^\circ

$$$$

b) Find $\angle VWT$.

Since $TW \parallel UV$, the interior angles on the same side of the transversal are supplementary. Therefore, $\angle V + \angle W = 180^\circ$.

$$$$

\angle V + \angle W = 180^\circ \\

57^\circ + \angle VWT = 180^\circ \\

\angle VWT = 180^\circ - 57^\circ \\

\angle VWT = 123^\circ

$$$$

3. Final Answer

a) $\angle TUV = 76^\circ$

b) $\angle VWT = 123^\circ$