Question

1. using the diagram below, classify the angle pairs as corresponding, alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.

a. ∠4 and ∠7
b. ∠2 and ∠11
c. ∠6 and ∠16
d. ∠8 and ∠13
e. ∠11 and ∠15
f. ∠7 and ∠10
g. ∠9 and ∠14
h. ∠12 and ∠15
i. ∠6 and ∠7
j. ∠1 and ∠3
k. ∠14 and ∠16
l. ∠6 and ∠15
m. ∠5 and ∠10
n. ∠8 and ∠14

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position at each intersection where a straight - line crosses two others. Alternate interior angles are between the two lines and on opposite sides of the transversal. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Consecutive interior angles are between the two lines and on the same side of the transversal. Consecutive exterior angles are outside the two lines and on the same side of the transversal.

Step2: Analyze each angle - pair

a. ∠4 and ∠7 are consecutive interior angles (CSSIA likely means Consecutive Same - Side Interior Angles).
b. ∠2 and ∠11 are alternate exterior angles.
c. ∠6 and ∠16 are corresponding angles.
d. ∠8 and ∠13 are alternate interior angles.
e. ∠11 and ∠15 are corresponding angles.
f. ∠7 and ∠10 are alternate exterior angles.
g. ∠9 and ∠14 are consecutive exterior angles (CSSEA likely means Consecutive Same - Side Exterior Angles).
h. ∠12 and ∠15 are consecutive interior angles.
i. ∠6 and ∠7 are consecutive exterior angles.
j. ∠1 and ∠3 are none (they are vertical angles).
k. ∠14 and ∠16 are none (no special transversal - related relationship).
l. ∠6 and ∠15 are none (no special transversal - related relationship).
m. ∠5 and ∠10 are corresponding angles.
n. ∠8 and ∠14 are none (no special transversal - related relationship).

Answer:

a. Consecutive interior angles
b. Alternate exterior angles
c. Corresponding angles
d. Alternate interior angles
e. Corresponding angles
f. Alternate exterior angles
g. Consecutive exterior angles
h. Consecutive interior angles
i. Consecutive exterior angles
j. None
k. None
l. None
m. Corresponding angles
n. None