Question

name that angle pair! determine whether the angles pairs are corresponding, alternate interior, alternate exterior, consecutive (same - side) interior, consecutive (same - side) exterior, or no relationship. corresponding angles: alternate interior angles: alternate exterior angles: consecutive interior angles: consecutive exterior angles: no relationship: ∠2 and ∠13 ∠4 and ∠11 ∠1 and ∠16 ∠3 and ∠12 ∠3 and ∠5 ∠14 and ∠16 n/a ∠1 and ∠3 ∠5 and ∠10 alt ex ∠3 and ∠15 n/a ∠4 and ∠5 ∠6 and ∠13 ∠4 and ∠13 alt int ∠2 and ∠8 n/a ∠4 and ∠12 n/a ∠3 and ∠16 ∠12 and ∠14 n/a con ∠7 and ∠15 ∠6 and ∠16 ∠11 and ∠14 ∠1 and ∠10 ex ∠1 and ∠11 ∠8 and ∠15 ∠7 and ∠13 n/a ∠1 and ∠14 n/a

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

• $\angle2$ and $\angle13$: No Relationship. They are not in any of the special angle - pair positions.
• $\angle4$ and $\angle11$: No Relationship.
• $\angle1$ and $\angle16$: No Relationship.
• $\angle3$ and $\angle12$: No Relationship.
• $\angle3$ and $\angle5$: Consecutive Interior Angles. They are between the two lines and on the same side of the transversal.
• $\angle14$ and $\angle16$: No Relationship.
• $\angle1$ and $\angle3$: No Relationship.
• $\angle5$ and $\angle10$: Alternate Exterior Angles. They are outside the two lines and on opposite sides of the transversal.
• $\angle3$ and $\angle15$: No Relationship.
• $\angle4$ and $\angle5$: No Relationship.
• $\angle6$ and $\angle13$: No Relationship.
• $\angle4$ and $\angle13$: Alternate Interior Angles. They are between the two lines and on opposite sides of the transversal.
• $\angle2$ and $\angle8$: No Relationship.
• $\angle4$ and $\angle12$: No Relationship.
• $\angle3$ and $\angle16$: No Relationship.
• $\angle12$ and $\angle14$: No Relationship.
• $\angle7$ and $\angle15$: Corresponding Angles. They are in the same relative position at each intersection where a straight - line crosses two others.
• $\angle6$ and $\angle16$: No Relationship.
• $\angle11$ and $\angle14$: No Relationship.
• $\angle1$ and $\angle10$: Consecutive Exterior Angles. They are outside the two lines and on the same side of the transversal.
• $\angle1$ and $\angle11$: No Relationship.
• $\angle8$ and $\angle15$: No Relationship.
• $\angle7$ and $\angle13$: No Relationship.
• $\angle1$ and $\angle14$: No Relationship.

Answer:

Corresponding Angles: $\angle7$ and $\angle15$
Alternate Interior Angles: $\angle4$ and $\angle13$
Alternate Exterior Angles: $\angle5$ and $\angle10$
Consecutive Interior Angles: $\angle3$ and $\angle5$
Consecutive Exterior Angles: $\angle1$ and $\angle10$
No Relationship: $\angle2$ and $\angle13$, $\angle4$ and $\angle11$, $\angle1$ and $\angle16$, $\angle3$ and $\angle12$, $\angle14$ and $\angle16$, $\angle1$ and $\angle3$, $\angle3$ and $\angle15$, $\angle4$ and $\angle5$, $\angle6$ and $\angle13$, $\angle2$ and $\angle8$, $\angle4$ and $\angle12$, $\angle3$ and $\angle16$, $\angle12$ and $\angle14$, $\angle6$ and $\angle16$, $\angle11$ and $\angle14$, $\angle1$ and $\angle11$, $\angle8$ and $\angle15$, $\angle7$ and $\angle13$, $\angle1$ and $\angle14$