Question

1. 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. ∠12 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. 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 between lines \(s\) and \(r\) and on the same side of transversal \(q\), so they are consecutive interior angles.

Step3: Analyze ∠2 and ∠11

They are outside lines \(r\) and \(s\) and on opposite sides of transversal \(p\), so they are alternate exterior angles.

Step4: Analyze ∠12 and ∠16

They are in the same relative position with respect to lines \(s\) and \(r\) and transversal \(q\), so they are corresponding angles.

Step5: Analyze ∠8 and ∠13

They are between lines \(s\) and \(r\) and on opposite sides of transversal \(q\), so they are alternate interior angles.

Step6: Analyze ∠11 and ∠15

They are in the same relative position with respect to lines \(s\) and \(r\) and transversal \(p\), so they are corresponding angles.

Step7: Analyze ∠7 and ∠10

They are between lines \(s\) and \(r\) and on opposite sides of transversal \(q\), so they are alternate interior angles.

Step8: Analyze ∠1 and ∠14

They are outside lines \(r\) and \(s\) and on opposite sides of transversal \(p\), so they are alternate exterior angles.

Step9: Analyze ∠12 and ∠15

They are between lines \(s\) and \(r\) and on the same side of transversal \(q\), so they are consecutive interior angles.

Step10: Analyze ∠6 and ∠7

They are outside lines \(r\) and \(s\) and on the same side of transversal \(q\), so they are none of the above - named angle - pairs.

Step11: Analyze ∠1 and ∠3

They are outside lines \(r\) and \(s\) and on the same side of transversal \(p\), so they are none of the above - named angle - pairs.

Step12: Analyze ∠12 and ∠16 (already done in Step 4)

They are corresponding angles.

Step13: Analyze ∠6 and ∠15

They are between lines \(r\) and \(s\) and on opposite sides of transversal \(q\), so they are alternate interior angles.

Step14: Analyze ∠5 and ∠10

They are in the same relative position with respect to lines \(r\) and \(s\) and transversal \(p\), so they are corresponding angles.

Step15: Analyze ∠8 and ∠14

They are outside lines \(r\) and \(s\) and on the same side of transversal \(q\), so they are none of the above - named angle - pairs.

Answer:

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