Question

using the diagram below, classify the angle pairs as corresponding, alternate interior, alternate exterior, consecutive interior, or none.
a. ∠4 and ∠7
b. ∠2 and ∠11
c. ∠12 and ∠16
d. ∠8 and ∠13
e. ∠11 and ∠15
f. ∠7 and ∠10
g. ∠1 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. 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.

Step2: Analyze ∠4 and ∠7

They are vertical angles, so the answer is none.

Step3: Analyze ∠2 and ∠11

They are alternate exterior angles.

Step4: Analyze ∠12 and ∠16

They are corresponding angles.

Step5: Analyze ∠8 and ∠13

They are alternate interior angles.

Step6: Analyze ∠11 and ∠15

They are corresponding angles.

Step7: Analyze ∠7 and ∠10

They are consecutive interior angles.

Step8: Analyze ∠1 and ∠14

They are corresponding angles.

Step9: Analyze ∠12 and ∠15

They are consecutive interior angles.

Step10: Analyze ∠6 and ∠7

They are alternate exterior angles.

Step11: Analyze ∠1 and ∠3

They are none.

Step12: Analyze ∠14 and ∠16

They are vertical angles, so the answer is none.

Step13: Analyze ∠6 and ∠15

They are none.

Step14: Analyze ∠5 and ∠10

They are alternate interior angles.

Step15: Analyze ∠8 and ∠14

They are corresponding angles.

Answer:

a. none
b. alternate exterior
c. corresponding
d. alternate interior
e. corresponding
f. consecutive interior
g. corresponding
h. consecutive interior
i. alternate exterior
j. none
k. none
l. none
m. alternate interior
n. corresponding