Question

answer the following questions. each question is worth 2 points. the diagram below has one set of parallel lines: 1. <4 and <5 are alternate interior angles, what is another pair of alternate interior angles? 2. alternate interior angles are choose an option 3. <1 and < 8 are alternate exterior angles, what is another pair of alternate exterior angles? 4. alternate exterior angles are choose an option 5. <1 and <4 are vertical angles, <6 and <____ is another pair of vertical angles? 6. vertical angles are choose an option 7. <1 and < 5 are corresponding angles, what angle would correspond with< 3? 8. corresponding angles are choose an option 9. <3 and < 5 are consecutive interior angles, what is another pair of consecutive interior angles? 10. consecutive interior angles are choose an option

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are between the parallel lines and on opposite sides of the transversal. In the given diagram with parallel lines \(L\) and \(m\) and transversal \(t\), \(\angle3\) and \(\angle6\) are another pair of alternate - interior angles.

Step2: Recall alternate - exterior angles definition

Alternate - exterior angles are outside the parallel lines and on opposite sides of the transversal. So, \(\angle2\) and \(\angle7\) are another pair of alternate - exterior angles.

Step3: Recall vertical angles definition

Vertical angles are opposite each other when two lines intersect. Since \(\angle1\) and \(\angle4\) are vertical angles, \(\angle6\) and \(\angle7\) are another pair of vertical angles.

Step4: Recall corresponding angles definition

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. \(\angle1\) and \(\angle5\) are corresponding angles, and \(\angle3\) corresponds to \(\angle7\).

Step5: Recall consecutive - interior angles definition

Consecutive - interior angles are between the parallel lines and on the same side of the transversal. So, \(\angle4\) and \(\angle5\) are another pair of consecutive - interior angles.

Answer:

1. \(\angle3\) and \(\angle6\)
2. Angles between parallel lines, opposite sides of transversal
3. \(\angle2\) and \(\angle7\)
4. Angles outside parallel lines, opposite sides of transversal
5. \(\angle7\)
6. Opposite angles when two lines intersect
7. \(\angle7\)
8. Angles in same relative position
9. \(\angle4\) and \(\angle5\)
10. Angles between parallel lines, same side of transversal