Question

directions: given the diagram below, determine whether the angle pairs are corresponding, alternate interior, alternate exterior, consecutive (same - side) interior, consecutive (same - side) exterior, or no relationship. color the boxes using the color codes below. corresponding angles: pink; alternate interior angles: light blue; alternate exterior angles: yellow; consecutive interior angles: light green; consecutive exterior angles: orange; no relationship: uncolored. ∠2 and ∠13, ∠4 and ∠11, ∠1 and ∠16, ∠3 and ∠12, ∠3 and ∠5, ∠14 and ∠16, ∠1 and ∠3, ∠5 and ∠10, ∠3 and ∠15, ∠4 and ∠5, ∠6 and ∠13, ∠4 and ∠13, ∠2 and ∠8, ∠4 and ∠12, ∠3 and ∠16, ∠12 and ∠14, ∠7 and ∠15, ∠6 and ∠16, ∠11 and ∠14, ∠1 and ∠10, ∠1 and ∠11, ∠8 and ∠15, ∠7 and ∠13, ∠1 and ∠14. ©gina wilson (all things algebra®, llc). 2014 - 2019

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position, alternate interior angles are between the lines and on opposite sides of the transversal, alternate exterior angles are outside the lines and on opposite sides of the transversal, consecutive interior angles are between the lines and on the same - side of the transversal, consecutive exterior angles are outside the lines and on the same - side of the transversal.

Step2: Analyze ∠2 and ∠13

They are between the lines and on opposite sides of the transversal, so they are alternate interior angles (Light Blue).

Step3: Analyze ∠4 and ∠11

They are between the lines and on the same - side of the transversal, so they are consecutive interior angles (Light Green).

Step4: Analyze ∠1 and ∠16

They have no special angle - pair relationship, so uncolored.

Step5: Analyze ∠3 and ∠12

They are outside the lines and on the same - side of the transversal, so they are consecutive exterior angles (Orange).

Step6: Analyze ∠3 and ∠5

They are between the lines and on the same - side of the transversal, so they are consecutive interior angles (Light Green).

Step7: Analyze ∠14 and ∠16

They are in the same relative position, so they are corresponding angles (Pink).

Step8: Analyze ∠1 and ∠3

They are in the same relative position, so they are corresponding angles (Pink).

Step9: Analyze ∠5 and ∠10

They have no special angle - pair relationship, so uncolored.

Step10: Analyze ∠3 and ∠15

They are in the same relative position, so they are corresponding angles (Pink).

Step11: Analyze ∠4 and ∠5

They are between the lines and on the same - side of the transversal, so they are consecutive interior angles (Light Green).

Step12: Analyze ∠6 and ∠13

They are between the lines and on opposite sides of the transversal, so they are alternate interior angles (Light Blue).

Step13: Analyze ∠4 and ∠13

They have no special angle - pair relationship, so uncolored.

Step14: Analyze ∠2 and ∠8

They are outside the lines and on opposite sides of the transversal, so they are alternate exterior angles (Yellow).

Step15: Analyze ∠4 and ∠12

They are in the same relative position, so they are corresponding angles (Pink).

Step16: Analyze ∠3 and ∠16

They have no special angle - pair relationship, so uncolored.

Step17: Analyze ∠12 and ∠14

They have no special angle - pair relationship, so uncolored.

Step18: Analyze ∠7 and ∠15

They are in the same relative position, so they are corresponding angles (Pink).

Step19: Analyze ∠6 and ∠16

They have no special angle - pair relationship, so uncolored.

Step20: Analyze ∠11 and ∠14

They have no special angle - pair relationship, so uncolored.

Step21: Analyze ∠1 and ∠10

They have no special angle - pair relationship, so uncolored.

Step22: Analyze ∠1 and ∠11

They have no special angle - pair relationship, so uncolored.

Step23: Analyze ∠8 and ∠15

They have no special angle - pair relationship, so uncolored.

Step24: Analyze ∠7 and ∠13

They have no special angle - pair relationship, so uncolored.

Step25: Analyze ∠1 and ∠14

They have no special angle - pair relationship, so uncolored.

Answer:

Angle Pairs	Relationship	Color
∠4 and ∠11	Consecutive Interior	Light Green
∠1 and ∠16	No Relationship	Uncolored
∠3 and ∠12	Consecutive Exterior	Orange
∠3 and ∠5	Consecutive Interior	Light Green
∠14 and ∠16	Corresponding	Pink
∠1 and ∠3	Corresponding	Pink
∠5 and ∠10	No Relationship	Uncolored
∠3 and ∠15	Corresponding	Pink
∠4 and ∠5	Consecutive Interior	Light Green
∠6 and ∠13	Alternate Interior	Light Blue
∠4 and ∠13	No Relationship	Uncolored
∠2 and ∠8	Alternate Exterior	Yellow
∠4 and ∠12	Corresponding	Pink
∠3 and ∠16	No Relationship	Uncolored
∠12 and ∠14	No Relationship	Uncolored
∠7 and ∠15	Corresponding	Pink
∠6 and ∠16	No Relationship	Uncolored
∠11 and ∠14	No Relationship	Uncolored
∠1 and ∠10	No Relationship	Uncolored
∠1 and ∠11	No Relationship	Uncolored
∠8 and ∠15	No Relationship	Uncolored
∠7 and ∠13	No Relationship	Uncolored
∠1 and ∠14	No Relationship	Uncolored