Question

question 4
which of the following represent the alternate interior angles of the given figure:
figure with two parallel lines j and k, and a transversal t creating angles 1,2,3,4 on j and 5,6,7,8 on k
options:
○ 5 and 3
○ 1 and 7
○ 2 and 7
○ 6 and 8

Explanation:

Step1: Recall Alternate Interior Angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two lines and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 5 and 3: Angle 5 is above line \( k \), angle 3 is below line \( j \). Not between the lines. Eliminate.
• Option 1 and 7: Angle 1 is above line \( j \) (left), angle 7 is below line \( k \) (right). Not between the lines. Eliminate.
• Option 2 and 7: Angle 2 is between lines \( j \) and \( k \) (right of transversal), angle 7 is between lines \( j \) and \( k \) (left of transversal). These are alternate interior angles.
• Option 6 and 8: These are vertical angles (adjacent, opposite), not alternate interior. Eliminate.

Answer:

2 and 7 (the option with "2 and 7")