Answer:
∠ TUW = ∠ SVW Proved.
Explanation:
See the diagram.
It is given that, ∠ VSW = ∠ WTU and SV ║ TU.
We have to prove that ∠ TUW = ∠ SVW
Statement 1. ∠ VSW = ∠ WTU and SV ║ TU.
Reason 1. It is given
Statement 2. ∠ VSW = ∠ TUW
Reason 2. They are alternate angles because SV ║ TU and SU is a transverse line.
Statement 3. ∠ WTU = ∠ SVW
Reason 3. They are alternate angles because SV ║ TU and VT is a transverse line.
Statement 4. ∠ VSW = ∠ SVW
Reason 4. Since ∠ TUW = ∠ SVW and ∠ VSW = ∠ TUW
Statement 5. ∠ TUW = ∠ SVW
Reason 5. Since ∠ VSW = ∠ TUW and ∠ VSW = ∠ SVW
(Answer)