Directions: If I || m, classify the marked angle pair and give their relationship, then solve for x.

Answer/Step-by-step explanation:

1. If l is parallel to m, therefore:

58° and (5x - 2)° are Corresponding Angles.

Relationship: 58° = (5x - 2)°

Solve for x

58 = 5x - 2

Add 2 to both sides

58 + 2 = 5x - 2 + 2

60 = 5x

Divide both sides by 5

60/5 = 5x/5

12 = x

x = 12

2. If l is parallel to m, therefore:

134° and (16x + 22)° are Alternate Exterior Angles.

Relationship: 134° = (16x + 22)°

Solve for x

134° = 16x + 22°

Subtract 22 from both sides

134 - 22 = 16x + 22 - 22

112 = 16x

Divide both sides by 16

112/16 = 16x/16

7 = x

x = 7

3. (7x - 1)° and 125° are Alternate Interior Angles.

Relationship: (7x - 1)° = 125°

Solve for x

7x - 1 = 125

Add 1 to both side

7x = 125 + 1

7x = 126

Divide both sides by 7

x = 18

4. (9x + 2)° and 133° are Same Side Interior Angles.

Relationship: (9x + 2)° + 133° = 180° (supplementary)

Solve for x

9x + 2 + 133 = 180

9x + 135 = 180

9x = 180 - 135

9x = 45

x = 5

5. (8x - 77)° and (3x + 38)° are Alternate Exterior Angles

Relationship: (8x - 77)° = (3x + 38)°

Solve for x

8x - 77 = 3x + 38

8x - 3x = 77 + 38

5x = 115

x = 23

6. (11x - 47)° and (6x - 2)° are Corresponding Angles.

Relationship: (11x - 47)° = (6x - 2)°

Solve for x

11x - 47 = 6x - 2

11x - 6x = 47 - 2

5x = 45

x = 9

7. (13x - 21)° and (5x + 75)° are Alternate Interior Angles.

Relationship: (13x - 21)° = (5x + 75)°

Solve for x

13x - 21 = 5x + 75

13x - 5x = 21 + 75

8x = 96

Divide both sides by 8

8x/8 = 96/8

x = 12

8. (9x - 33)° and (5x + 3)° are Consecutive Exterior Angles

Relationship: (9x - 33)° + (5x + 3)° = 180°

Solve for x

9x - 33 + 5x + 3 = 180

14x - 30 = 180

14x = 180 + 30

14x = 210

x = 15