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

Explanation:

Step1: Recall angle - pair relationships

Corresponding angles are in the same relative position at each intersection. 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 ∠2 and ∠13

They are alternate interior angles. So the color is light blue (LB).

Step3: Analyze ∠4 and ∠11

They are consecutive interior angles. So the color is light green (LG).

Step4: Analyze ∠1 and ∠16

They have no relationship. So it is uncolored.

Step5: Analyze ∠3 and ∠12

They are consecutive exterior angles. So the color is orange (CE).

Step6: Analyze ∠3 and ∠5

They are consecutive interior angles. So the color is light green (LG).

Step7: Analyze ∠14 and ∠16

They are corresponding angles. So the color is pink (P).

Step8: Analyze ∠1 and ∠3

They are corresponding angles. So the color is pink (P).

Step9: Analyze ∠5 and ∠10

They have no relationship. So it is uncolored.

Step10: Analyze ∠3 and ∠15

They are corresponding angles. So the color is pink (P).

Step11: Analyze ∠4 and ∠5

They are consecutive interior angles. So the color is light green (LG).

Step12: Analyze ∠6 and ∠13

They are alternate interior angles. So the color is light blue (LB).

Step13: Analyze ∠4 and ∠13

They have no relationship. So it is uncolored.

Step14: Analyze ∠2 and ∠8

They are alternate exterior angles. So the color is yellow (Y).

Step15: Analyze ∠4 and ∠12

They are corresponding angles. So the color is pink (P).

Step16: Analyze ∠3 and ∠16

They have no relationship. So it is uncolored.

Step17: Analyze ∠12 and ∠14

They have no relationship. So it is uncolored.

Step18: Analyze ∠7 and ∠15

They are corresponding angles. So the color is pink (P).

Step19: Analyze ∠6 and ∠16

They have no relationship. So it is uncolored.

Step20: Analyze ∠11 and ∠14

They have no relationship. So it is uncolored.

Step21: Analyze ∠1 and ∠10

They have no relationship. So it is uncolored.

Step22: Analyze ∠1 and ∠11

They have no relationship. So it is uncolored.

Step23: Analyze ∠8 and ∠15

They have no relationship. So it is uncolored.

Step24: Analyze ∠7 and ∠13

They have no relationship. So it is uncolored.

Step25: Analyze ∠1 and ∠14

They have no relationship. So it is uncolored.

Answer:

Angle Pairs	Relationship/Color
∠4 and ∠11	Light Green (LG) - Consecutive Interior
∠1 and ∠16	Uncolored - No Relationship
∠3 and ∠12	Orange (CE) - Consecutive Exterior
∠3 and ∠5	Light Green (LG) - Consecutive Interior
∠14 and ∠16	Pink (P) - Corresponding
∠1 and ∠3	Pink (P) - Corresponding
∠5 and ∠10	Uncolored - No Relationship
∠3 and ∠15	Pink (P) - Corresponding
∠4 and ∠5	Light Green (LG) - Consecutive Interior
∠6 and ∠13	Light Blue (LB) - Alternate Interior
∠4 and ∠13	Uncolored - No Relationship
∠2 and ∠8	Yellow (Y) - Alternate Exterior
∠4 and ∠12	Pink (P) - Corresponding
∠3 and ∠16	Uncolored - No Relationship
∠12 and ∠14	Uncolored - No Relationship
∠7 and ∠15	Pink (P) - Corresponding
∠6 and ∠16	Uncolored - No Relationship
∠11 and ∠14	Uncolored - No Relationship
∠1 and ∠10	Uncolored - No Relationship
∠1 and ∠11	Uncolored - No Relationship
∠8 and ∠15	Uncolored - No Relationship
∠7 and ∠13	Uncolored - No Relationship
∠1 and ∠14	Uncolored - No Relationship