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

They are consecutive interior angles as they are between the two lines and on the same side of the transversal.

b. ∠2 and ∠11

They are alternate exterior angles as they are outside the two lines and on opposite sides of the transversal.

c. ∠6 and ∠16

They are corresponding angles as they are in the same relative position at each intersection where a transversal crosses two lines.

d. ∠8 and ∠13

They are alternate interior angles as they are between the two lines and on opposite sides of the transversal.

e. ∠11 and ∠15

They are consecutive exterior angles as they are outside the two lines and on the same side of the transversal.

f. ∠7 and ∠10

They are none of the above - mentioned types.

g. ∠9 and ∠14

They are none of the above - mentioned types.

h. ∠12 and ∠15

They are consecutive interior angles as they are between the two lines and on the same side of the transversal.

i. ∠6 and ∠7

They are none of the above - mentioned types.

j. ∠1 and ∠3

They are none of the above - mentioned types.

k. ∠14 and ∠16

They are none of the above - mentioned types.

l. ∠6 and ∠15

They are none of the above - mentioned types.

m. ∠5 and ∠10

They are none of the above - mentioned types.

n. ∠8 and ∠14

They are none of the above - mentioned types.

Answer:

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