Question

proving lines parallel
find the measure of the indicated angle that makes lines u and v parallel.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Recall parallel - line angle rules

When two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Solve for each angle

1)

If the lines $u$ and $v$ are parallel, the angle corresponding to the $130^{\circ}$ angle (or the alternate - interior angle) is also $130^{\circ}$.

2)

The angle corresponding to the $128^{\circ}$ angle (or the alternate - interior angle) is $128^{\circ}$.

3)

The angle corresponding to the $66^{\circ}$ angle (or the alternate - interior angle) is $66^{\circ}$.

4)

The angle corresponding to the $80^{\circ}$ angle (or the alternate - interior angle) is $80^{\circ}$.

5)

If the lines $u$ and $v$ are parallel, and there is a right - angle on line $v$, the corresponding angle on line $u$ is also $90^{\circ}$.

6)

The angle corresponding to the $81^{\circ}$ angle (or the alternate - interior angle) is $81^{\circ}$.

7)

The angle corresponding to the $53^{\circ}$ angle (or the alternate - interior angle) is $53^{\circ}$.

8)

The angle corresponding to the $58^{\circ}$ angle (or the alternate - interior angle) is $58^{\circ}$.

Answer:

1. $130^{\circ}$
2. $128^{\circ}$
3. $66^{\circ}$
4. $80^{\circ}$
5. $90^{\circ}$
6. $81^{\circ}$
7. $53^{\circ}$
8. $58^{\circ}$