Question

name santiago date 10/9/18 parallel lines cut by a transversal parallel lines l and m are intersected by line n. answer the following questions based on the information given. true/false 1. angles 1 and 3 are vertical angles. 2. the value of angle 7 is 125 degrees. 3. angles 1 and 6 are alternate interior angles. 4. angles 3 and 5 are alternate interior angles. 5. angles 4 and 8 are corresponding angles. 6. the value of angle 5 is 55 degrees. 7. angles 1 and 7 are alternate exterior angles. 8. angles 6 and 8 are corresponding angles. 9. angles 1 and 6 are supplementary angles. 10. angles 4 and 8 are supplementary angles.

Explanation:

Step1: Recall vertical - angles definition

Vertical angles are opposite each other when two lines intersect. Angles 1 and 3 are vertical angles. So, statement 1 is True.

Step2: Use angle - relationships in parallel lines

Corresponding angles are equal. Angle 7 and the 125 - degree angle are corresponding angles. So, the value of angle 7 is 125 degrees. Statement 2 is True.

Step3: Recall alternate - interior angles definition

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. Angles 1 and 6 are not alternate interior angles. So, statement 3 is False.

Step4: Recall alternate - interior angles definition

Angles 3 and 5 are alternate interior angles. So, statement 4 is True.

Step5: Recall corresponding angles definition

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. Angles 4 and 8 are corresponding angles. So, statement 5 is True.

Step6: Use angle - relationships in parallel lines

Corresponding angles are equal. Angle 5 and the 55 - degree angle are corresponding angles. So, the value of angle 5 is 55 degrees. Statement 6 is True.

Step7: Recall alternate - exterior angles definition

Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. Angles 1 and 7 are alternate exterior angles. So, statement 7 is True.

Step8: Recall corresponding angles definition

Angles 6 and 8 are not corresponding angles. So, statement 8 is False.

Step9: Recall supplementary - angles definition

Supplementary angles add up to 180 degrees. Angle 1 is 55 degrees and angle 6 is 55 degrees, so they are not supplementary. Statement 9 is False.

Step10: Recall supplementary - angles definition

Angles 4 and 8 are corresponding angles and are equal (both 125 degrees), not supplementary. Statement 10 is False.

Answer:

1. True
2. True
3. False
4. True
5. True
6. True
7. True
8. False
9. False
10. False