Question

which of the following statements and justifications would prove that t // u? answer attempt 1 out of 2 ∠1=∠7, by converse of alternate exterior angles ∠7 and ∠10 are supplementary, by converse of same - side interior angles ∠3 and ∠8 are supplementary, by converse of same - side interior angles ∠7 and ∠8 are supplementary, by converse of linear pairs

Explanation:

Step1: Recall parallel - line determination theorems

If alternate exterior angles are equal, the lines are parallel; if same - side interior angles are supplementary, the lines are parallel.

Step2: Analyze each option

• For $\angle1=\angle7$, by the converse of alternate exterior angles, if two alternate exterior angles are equal, the two lines ($t$ and $u$) are parallel.
• For $\angle7$ and $\angle10$ being supplementary, they are not same - side interior angles for lines $t$ and $u$.
• For $\angle3$ and $\angle8$ being supplementary, they are not same - side interior angles for lines $t$ and $u$.
• $\angle7$ and $\angle8$ being supplementary is by the property of linear pairs, not related to the parallelism of $t$ and $u$.

Answer:

$\angle1 = \angle7$, by Converse of Alternate Exterior Angles