Question

name the type of angle relationship. if no relationship exist, choose none. 1. angles 1 & 8: select 2. angles 2 & 3: select 3. angles 5 & 7: 4. angles 2 & 7: 5. angles 1 & 6: select

Explanation:

Step1: Recall angle - relationship definitions

• Alternate exterior angles: Angles that lie outside the two lines and on opposite sides of the transversal.
• Alternate interior angles: Angles that lie between the two lines and on opposite sides of the transversal.
• Consecutive interior angles: Angles that lie between the two lines and on the same side of the transversal.
• Corresponding angles: Angles that are in the same relative position with respect to the lines and the transversal.
• Vertical angles: Angles that are opposite each other when two lines intersect.

Step2: Analyze each pair

1. Angles 1 & 8:

• They lie outside the two lines \(p\) and \(q\) and on opposite sides of the transversal \(r\). So, they are alternate exterior angles.

1. Angles 2 & 3:

• They have no special angle - relationship as defined above.

1. Angles 5 & 7:

• They lie between the two lines \(p\) and \(q\) and on the same side of the transversal \(r\). So, they are consecutive interior angles.

1. Angles 2 & 7:

• They lie between the two lines \(p\) and \(q\) and on opposite sides of the transversal \(r\). So, they are alternate interior angles.

1. Angles 1 & 6:

• They are opposite each other when two lines (the lines forming the angles) intersect. So, they are vertical angles.

Answer:

1. alt. exterior
2. none
3. consecutive interior
4. alt. interior
5. vertical