Question

Activity The image shows a transversal passing through two parallel lines. Use it to answer the questions that follow. S T U W N Part A 4 Write the 16 pairs of supplementary angles in the table.

Answer 1

The 16 pairs of supplementary angles for the two parallel lines include the following;

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

In Mathematics and Euclidean Geometry, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both intersect at a point or form a linear pair.

By applying the linear pair theorem to the figure, we can logically deduce the following supplementary angles:

1. S and V
2. S and T
3. V and U
4. U and T
5. Z and W
6. Y and X
7. W and X
8. Z and Y

By applying the converse of same side interior angles postulate, we have the following supplementary angles:

1. T and W
2. U and Z

By applying the converse of same side exterior angles postulate, we have the following supplementary angles:

1. S and X
2. V and Y

Based on the transversal cutting through the two parallel lines, we have the following supplementary angles:

1. S and Z
2. V and W
3. T and Y
4. U and X

Answer 2

we know that

Supplementary angles are angles that their sum is equal to 180 degrees

so

In this problem we have

V and S

S and T

T and U

U and V

U and Z

T and W

Z and Y

Y and X

X and W

Z and W

X and S

Y and V

X and S

U and Y

W and V

S and Z