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. ∠5 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 definitions

• Corresponding angles: In matching positions relative to transversal and parallel lines.
• Alternate interior angles: Between parallel lines and on opposite sides of transversal.
• Alternate exterior angles: Outside parallel lines and on opposite sides of transversal.
• Consecutive interior angles: Between parallel lines and on same side of transversal.

Step2: Analyze each pair

• a. $\angle4$ and $\angle7$: Alternate interior (between lines \(r\) and \(s\), opposite sides of transversal \(p\)).
• b. $\angle2$ and $\angle11$: None (no defined relation).
• c. $\angle12$ and $\angle16$: Alternate exterior (outside lines \(r\) and \(s\), opposite sides of transversal \(p\)).
• d. $\angle8$ and $\angle13$: None (no defined relation).
• e. $\angle11$ and $\angle15$: Alternate exterior (outside lines \(r\) and \(s\), opposite sides of transversal \(q\)).
• f. $\angle7$ and $\angle10$: Alternate interior (between lines \(r\) and \(s\), opposite sides of transversal \(q\)).
• g. $\angle1$ and $\angle14$: Alternate exterior (outside lines \(r\) and \(s\), opposite sides of transversal \(q\)).
• h. $\angle12$ and $\angle15$: None (no defined relation).
• i. $\angle6$ and $\angle7$: Consecutive interior (between lines \(r\) and \(s\), same side of transversal \(q\)).
• j. $\angle1$ and $\angle3$: Corresponding (matching positions relative to transversals).
• k. $\angle12$ and $\angle16$: Alternate exterior (already done in c).
• l. $\angle6$ and $\angle15$: Corresponding (matching positions relative to transversals).
• m. $\angle5$ and $\angle10$: Consecutive interior (between lines \(r\) and \(s\), same side of transversal \(q\)).
• n. $\angle8$ and $\angle14$: Corresponding (matching positions relative to transversals).

Answer:

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