Question

activity
the image shows a transversal passing through two parallel lines. use it to answer the questions that follow.
part a
write the 16 pairs of supplementary angles in the table.

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°. When a transversal intersects two parallel lines, linear - pair angles and same - side interior angles are supplementary.

Step2: Identify linear - pair supplementary angles

At the intersection of the transversal with the first line:

• $\angle S$ and $\angle T$ (linear pair), $\angle T$ and $\angle U$ (linear pair), $\angle U$ and $\angle V$ (linear pair), $\angle V$ and $\angle S$ (linear pair).

At the intersection of the transversal with the second line:

• $\angle W$ and $\angle X$ (linear pair), $\angle X$ and $\angle Y$ (linear pair), $\angle Y$ and $\angle Z$ (linear pair), $\angle Z$ and $\angle W$ (linear pair).

Step3: Identify same - side interior supplementary angles

Same - side interior angles between the parallel lines:

• $\angle U$ and $\angle W$ (same - side interior), $\angle V$ and $\angle Z$ (same - side interior).

Also, considering the vertical - angle relationships and supplementary nature:

• $\angle S$ and $\angle X$ (since $\angle S=\angle U$ and $\angle U$ and $\angle W$ are supplementary, and $\angle W$ and $\angle X$ are linear - pair), $\angle T$ and $\angle Y$ (since $\angle T=\angle V$ and $\angle V$ and $\angle Z$ are supplementary, and $\angle Z$ and $\angle Y$ are linear - pair), $\angle U$ and $\angle X$ (vertical - angle related to linear - pair and supplementary relationships), $\angle V$ and $\angle Y$ (vertical - angle related to linear - pair and supplementary relationships), $\angle S$ and $\angle W$ (vertical - angle related to same - side interior supplementary), $\angle T$ and $\angle Z$ (vertical - angle related to same - side interior supplementary).

The 16 pairs of supplementary angles are:

1. $\angle S$ and $\angle T$
2. $\angle T$ and $\angle U$
3. $\angle U$ and $\angle V$
4. $\angle V$ and $\angle S$
5. $\angle W$ and $\angle X$
6. $\angle X$ and $\angle Y$
7. $\angle Y$ and $\angle Z$
8. $\angle Z$ and $\angle W$
9. $\angle U$ and $\angle W$
10. $\angle V$ and $\angle Z$
11. $\angle S$ and $\angle X$
12. $\angle T$ and $\angle Y$
13. $\angle U$ and $\angle X$
14. $\angle V$ and $\angle Y$
15. $\angle S$ and $\angle W$
16. $\angle T$ and $\angle Z$

Answer:

1. $\angle S$ and $\angle T$
2. $\angle T$ and $\angle U$
3. $\angle U$ and $\angle V$
4. $\angle V$ and $\angle S$
5. $\angle W$ and $\angle X$
6. $\angle X$ and $\angle Y$
7. $\angle Y$ and $\angle Z$
8. $\angle Z$ and $\angle W$
9. $\angle U$ and $\angle W$
10. $\angle V$ and $\angle Z$
11. $\angle S$ and $\angle X$
12. $\angle T$ and $\angle Y$
13. $\angle U$ and $\angle X$
14. $\angle V$ and $\angle Y$
15. $\angle S$ and $\angle W$
16. $\angle T$ and $\angle Z$