Question

number 4: identify the transversal connecting each pair of angles in the photo. then classify the relationship between each pair of angles.
a. ∠1 and ∠8
b. ∠3 and ∠6
c. ∠6 and ∠7
d. ∠3 and ∠1
e. ∠4 and ∠7

Explanation:

Step1: Recall angle - pair relationships

When two lines are cut by a transversal, different angle - pair relationships exist such as vertical angles, corresponding angles, alternate interior angles, alternate exterior angles, and same - side interior angles.

Step2: Analyze ∠1 and ∠8

∠1 and ∠8 are alternate exterior angles. They are on the outer side of the two lines cut by the transversal and on the opposite sides of the transversal.

Step3: Analyze ∠3 and ∠6

∠3 and ∠6 are alternate interior angles. They are on the inner side of the two lines cut by the transversal and on the opposite sides of the transversal.

Step4: Analyze ∠6 and ∠7

∠6 and ∠7 are same - side interior angles. They are on the inner side of the two lines cut by the transversal and on the same side of the transversal.

Step5: Analyze ∠3 and ∠1

∠3 and ∠1 are corresponding angles. They are in the same relative position with respect to the transversal and the two lines.

Step6: Analyze ∠4 and ∠7

∠4 and ∠7 are vertical angles. They are opposite each other when two lines intersect.

Answer:

a. Alternate exterior angles
b. Alternate interior angles
c. Same - side interior angles
d. Corresponding angles
e. Vertical angles